对称排它过程的扰动

对称排它过程中粒子流的一个极限定理

A limit theorem for particle current in the symmetric exclusion process

利用最近发现的对称排它过程的强负相关性质，我们推导出了区域间粒子的归一化电流收敛于高斯分布的一般条件。主要的新颖之处在于，结果不假设任何平移不变性，并持有大多数初始配置。

Variable speed symmetric random walk driven by symmetric exclusion

We prove a quenched functional central limit theorem for a one-dimensional random walk driven by a simple symmetric exclusion process. This model can be viewed as a special case of the random walk in a balanced random environment, for which the weak quenched limit is constructed as a function of the invariant measure of the environment viewed from the walk. We bypass the need to show the existence of this invariant measure. Instead, we find the limit of the quadratic variation of the walk and give an explicit formula for it.

Non-equilibrium and stationary fluctuations of a slowed boundary symmetric exclusion

We consider a one-dimensional symmetric simple exclusion process in contact with slowed reservoirs: at the left (resp. right) boundary, particles are either created or removed at rates given by $α/n$ or $(1-α)/n$ (resp. $β/n$ or $(1-β)/n$) where $α, β>0$ and $n$ is a scaling parameter. We obtain the non-equilibrium fluctuations and consequently the non-equilibrium stationary fluctuations.

Symmetric exclusion as a random environment: invariance principle

We establish an invariance principle for a one-dimensional random walk in a dynamical random environment given by a speed-change exclusion process. The jump probabilities of the walk depend on the configuration of the exclusion in a finite box around the walker. The environment starts from equilibrium. After a suitable space-time rescaling, the random walk converges to a sum of two independent processes, a Brownian motion and a Gaussian process with stationary increments.

Quantitative ergodicity for the symmetric exclusion process with stationary initial data

We consider the symmetric exclusion process on the $d$-dimensional lattice with translational invariant and ergodic initial data. It is then known that as $t$ diverges the distribution of the process at time $t$ converges to a Bernoulli product measure. Assuming a summable decay of correlations of the initial data, we prove a quantitative version of this convergence by obtaining an explicit bound on the Ornstein $\bar d$-distance. The proof is based on the analysis of a two species exclusion process with annihilation.

一维最近邻对称简单排斥中的分数布朗运动极限

On fractional Brownian motion limits in one dimensional nearest-neighbor symmetric simple exclusion

关于一维最近邻对称简单排它过程的一个著名结果是在有限维分布的意义下，穿过原点的亚扩散重标度电流和亚扩散重标度标记粒子位置收敛到Hurst参数为1/4的分数布朗运动.本文的目的是改进这种收敛到一个泛函中心极限定理，关于一致拓扑，并完成解决一个猜想在文献中关于简单的排斥过程。

具有自由边界的对称简单排它过程

Symmetric simple exclusion process with free boundaries

本文考虑一维对称简单排它过程（SSEP），它的生与死限制在最左边有一个洞和最右边有一个粒子的构形子集上.在最左边的洞的位置，粒子以固定的速率出生，而在同样的速率，最右边的粒子独立地死亡。我们证明了收敛到一个流体力学极限，并讨论了它与一个自由边界问题的关系。

作为随机环境的对称排斥：流体动力学极限

Symmetric exclusion as a random environment: hydrodynamic limits

考虑一维连续时间随机游动，其转移率依赖于一个从平衡态出发的简单的自治对称排它过程。该模型代表了缓慢非均匀混合动态随机环境中的随机游动的示例。在一个适当的空间-时间的重新标度，其中的排斥是加速相比，随机游动，我们证明了流体力学的极限定理的排斥，看到这个行走，我们推导出一个常微分方程描述的宏观演化的行走。主要的困难是证明的替代引理的排除，从行走没有明确的知识，其不变测度。我们进一步讨论如何获得类似的结果，这个模型的几个变种。

非椭圆动态随机电导的对称排斥模型

Symmetric exclusion as a model of non-elliptic dynamical random conductances

考虑任意维整数格上的有限值域对称排它过程。我们解释它作为一个非椭圆形的时间依赖性随机电导模型设置电导等于1的边缘与端点占据的粒子的排它过程和零的其他地方。利用Kipnis-Varhadan鞅近似，证明了由电导动力场驱动的随机游动的一个大数定律和一个中心极限定理.不像排它过程中的标记粒子，它在某种意义上类似于这个模型，这个随机游动是扩散的，即使在一维最近邻的情况下。

Hydrodynamic limit for a boundary driven super-diffusive symmetric exclusion

We study the hydrodynamic limit for a model of symmetric exclusion processes with heavy-tailed long jumps and in contact with infinitely extended reservoirs. We show how the corresponding hydrodynamic equations are affected by the parameters defining the model. The hydrodynamic equations are characterized by a class of super-diffusive operators that are given by the regional fractional Laplacian with some additional reaction terms and various boundary conditions. This work solves some questions left open in \cite{BJGO2} about the same model.

Hydrodynamic limit for a $d$-dimensional open symmetric exclusion process

In this paper we focus on the open symmetric exclusion process with parameter $m$ (open SEP($m/2$)), which allows $m$ particles each site and has an open boundary. We generalize the result about hydrodynamic limit for the open SEP$(m/2)$ that was originally raised in Theorem 4.12 of arXiv:1908.02359. We prove that the hydrodynamic limit of the density profile for a $d-$dimensional open SEP$(m/2)$ solves the $(d+1)-$dimensional heat equation with certain initial condition and boundary condition.

具有开放边界的广义对称排斥过程的流体动力学行为

Hydrodynamical behavior for the generalized symmetric exclusion with open boundary

本文研究了允许每个位置最多$α$个粒子的广义对称排斥过程，将其与强度由参数$θ$调节的随机水库接触，证明其流体动力学行为由热方程描述，且边界条件随$θ$变化，并在$α=1$时与已知结果一致。

对称排斥中的瞬态随机游动：极限定理和一个Einstein关系

Transient random walk in symmetric exclusion: limit theorems and an Einstein relation

我们考虑一个一维简单的对称排它过程的平衡，构成一个动态的随机环境的最近邻随机游动，在占用/空置网站有两个不同的本地漂移的权利。我们构建了一个更新结构，从一个LLN，一个功能CLT和退火措施下的随机游动的大偏差界如下。我们进一步证明了在适当的微扰下的爱因斯坦关系。本文讨论了慢混合动态随机环境中的随机游动问题。

Particle model for the reservoirs in the simple symmetric exclusion process

In this paper, we will study the long time behavior of the simple symmetric exclusion process in the ``channel'' $Λ_N=[1,N]\cap \mathbb{N}$ with reservoirs at the boundaries. These reservoirs are also systems of particles which can be exchanged with the particles in the channel. The size $M$ of each reservoir is much larger than the one of the channel, i.e. $M=N^{1+α}$ for a fixed number $α>0$. Based on the size of the channel and the holding time at each reservoir, we will investigate some types of rescaling time.

简单对称排他过程的一个定量中心极限定理

A quantitative central limit theorem for the simple symmetric exclusion process

本文通过比较 SSEP 密度涨落场与广义 Ornstein-Uhlenbeck 过程的生成元，并利用无穷维 Berry-Essen 界，证明了 d 维离散环面上简单对称排他过程的最优速率定量中心极限定理。

A Driven Tagged Particle in Symmetric Exclusion Processes with Removals

We consider a driven tagged particle in a symmetric exclusion process on Z with a removal rule. In this process, untagged particles are removed once they jump to the left of the tagged particle. We investigate the behavior of the displacement of the tagged particle and prove limit theorems of it: an (annealed) law of large numbers, a central limit theorem, and a large deviation principle. We also characterize a class of ergodic measures for the environment process. Our approach is based on analyzing two auxiliary processes with associated martingales and a regenerative structure.

对称排斥过程中电流与占据时间的非平衡联合涨落

Nonequilibrium Joint Fluctuations for Current and Occupation Time in The Symmetric Exclusion Process

本文研究一维非平衡 SSEP 中电流与占据时间的联合涨落，给出极限高斯过程协方差公式，并通过相关性估计、离散梯度估计和 Fourier 型 Kipnis–Varadhan 引理证明紧性。

对称排斥过程的混合与相应的单粒子随机游动

Mixing of the symmetric exclusion processes in terms of the corresponding single-particle random walk

我们证明了一个上界的对称排它过程的$\varepsilon$ -混合时间的任何图G，与任何可行的粒子数。我们的估计与$\mathsf{T}_{\mathsf{RW}(G)}\ln(|V|/\varepsilon)$成比例，其中|V|是G中的顶点数，$\mathsf{T}_{\mathsf{RW}(G)}$是相应的单粒子随机游动的1/4混合时间。这个界包含了$\mathbb{R}^d$中膨胀子、渗流簇、Erdos-Renyi随机图的巨分支和Poisson点过程的对称排斥的新结果.我们的技术工具包括莫里斯变色龙工艺的一种变体。

Explicit LDP for a slowed RW driven by a symmetric exclusion process

We consider a random walk (RW) driven by a simple symmetric exclusion process (SSE). Rescaling the RW and the SSE in such a way that a joint hydrodynamic limit theorem holds we prove a joint path large deviation principle. The corresponding large deviation rate function can be split into two components, the rate function of the SSE and the one of the RW given the path of the SSE. Such components have different structures (Gaussian and Poissoinian, respectively) and to overcome this difficulty we make use of the theory of Orlicz spaces. In particular, the component of the rate function correspo…

Moderate Deviations for the current and Tagged Particle in Symmetric Simple Exclusion Processes

We prove moderate deviation principles for the tagged particle position and current in one-dimensional symmetric simple exclusion processes. There is at most one particle per site. A particle jumps to one of its two neighbors at rate $1/2$, and the jump is suppressed if there is already one at the target site. We distinguish one particular particle which is called the tagged particle. We first establish a variational formula for the moderate deviation rate functions of the tagged particle positions based on moderate deviation principles from hydrodynamic limit proved by Gao and Quastel \cite{g…

Diffusive fluctuations of long-range symmetric exclusion with a slow barrier

In this article we obtain the equilibrium fluctuations of a symmetric exclusion process in $\mathbb{Z}$ with long jumps. The transition probability of the jump from $x$ to $y$ is proportional to $|x-y|^{-γ-1}$. Here we restrict to the choice $γ\geq 2$ so that the system has a diffusive behavior. Moreover, when particles move between $\mathbb{Z}_{-}^{*}$ and $\mathbb N$, the jump rates are slowed down by a factor $αn^{-β}$, where $α>0$, $β\geq 0$ and $n$ is the scaling parameter. Depending on the values of $β$ and $γ$, we obtain several stochastic partial differential equations, corresponding t…

对完备黎曼流形和主丛上对称排斥过程的水动力极限

Hydrodynamic limit of the symmetric exclusion process on complete Riemannian manifolds and principal bundles

研究在泊松随机邻域图逼近带下界曲率的加权黎曼流形上对称排斥过程的水动力极限，推导福克-规划方程，并扩展到主丛，得到带有加权水平拉普拉斯算子的福克-规划方程。

Corrigendum to: Phase transition in equilibrium fluctuations of symmetric slowed exclusion

We present the correct space of test functions for the Ornstein-Uhlenbeck processes defined in \cite{fgn2}. Under these new spaces, an invariance with respect to a second order operator is shown, granting the existence and uniqueness of those processes. Moreover, we detail how to prove some properties of the semi-groups, which are required in the proof of uniqueness.

边界驱动对称简单排斥过程中稀有事件的首中时

Hitting times of rare events in boundary driven symmetric simple exclusion processes

在边界驱动的对称简单排斥过程中，考虑一个不包含稳态密度分布的密度分布开集$\ms O$。我们证明了第一次访问集合$\ms O$的经验措施收敛到一个指数分布。

Monotonicity properties of exclusion sensitivity

In~\cite{bgs2013}, exclusion sensitivity and exclusion stability for symmetric exclusion processes on graphs were defined as a natural analogue of noise sensitivity and noise stability in this setting. As these concepts were defined for any sequence of connected graphs, it is natural to study the monotonicity properties of these definitions with respect to adding edges to the graphs, and in particular, whether some graphs are more stable or sensitive than others. The main purpose of this paper is to answer some such question from~\cite{bgs2013}. The main tool used is included results about the…

对称与提升简单排他模型的直径

Diameters of symmetric and lifted simple exclusion models

本文确定了一维N粒子排他模型（Ssep和提升的Tasep）马尔可夫链的直径，为混合时间提供下界，并探讨了其对模型分析的意义。

边界驱动对称简单排斥过程的定态非平衡测度的熵

Entropy of stationary nonequilibrium measures of boundary driven symmetric simple exclusion processes

本文研究了边界驱动对称简单排斥过程的定态非平衡测度的熵。与Gibbs-Shannon熵\cite{B, DLS2}不同，非平衡定态的熵不同于局域平衡态的熵。

Dynamical large deviations for the boundary driven symmetric exclusion process with Robin boundary conditions

In this article, we consider a one-dimensional symmetric exclusion process in weak contact with reservoirs at the boundary. In the diffusive time-scaling the empirical measure evolves according to the heat equation with Robin boundary conditions. We prove the associated dynamical large deviations principle.

Hydrodynamics for symmetric exclusion in contact with reservoirs

We consider the symmetric exclusion process with jumps given by a symmetric, translation invariant, transition probability $p(\cdot)$. The process is put in contact with stochastic reservoirs whose strength is tuned by a parameter $θ\in\mathbb R$. Depending on the value of the parameter $θ$ and the range of the transition probability $p(\cdot)$ we obtain the hydrodynamical behavior of the system. The type of hydrodynamic equation depends on whether the underlying probability $p(\cdot)$ has finite or infinite variance and the type of boundary condition depends on the strength of the stochastic …

对称排它过程的分布极限

Distributional Limits for the Symmetric Exclusion Process

最近证明了对称排它过程的强负相关性质。在本文中，我们应用这些结果来证明收敛到泊松和正态分布的各种泛函的过程。

Symmetric simple exclusion process in dynamic environment: hydrodynamics

We consider the symmetric simple exclusion process in $\mathbb Z^d$ with quenched bounded dynamic random conductances and prove its hydrodynamic limit in path space. The main tool is the connection, due to the self-duality of the process, between the invariance principle for single particles starting from all points and the macroscopic behavior of the density field. While the hydrodynamic limit at fixed macroscopic times is obtained via a generalization to the time-inhomogeneous context of the strategy introduced in \cite{nagy_symmetric_2002}, in order to prove tightness for the sequence of em…

Coalescing and branching simple symmetric exclusion process

Motivated by kinetically constrained interacting particle systems (KCM), we consider a reversible coalescing and branching simple exclusion process on a general finite graph $G=(V,E)$ dual to the biased voter model on $G$. Our main goal are tight bounds on its logarithmic Sobolev constant and relaxation time, with particular focus on the delicate slightly supercritical regime in which the equilibrium density of particles tends to zero as $|V|\rightarrow \infty$. Our results allow us to recover very directly and improve to $\ell^p$-mixing, $p\ge 2$, and to more general graphs, the mixing time r…

Random walk on the simple symmetric exclusion process

We investigate the long-term behavior of a random walker evolving on top of the simple symmetric exclusion process (SSEP) at equilibrium, in dimension one. At each jump, the random walker is subject to a drift that depends on whether it is sitting on top of a particle or a hole, so that its asymptotic behavior is expected to depend on the density $ρ\in [0, 1]$ of the underlying SSEP. Our first result is a law of large numbers (LLN) for the random walker for all densities $ρ$ except for at most two values $ρ_-, ρ_+ \in [0, 1]$. The asymptotic speed we obtain in our LLN is a monotone function of…

随机环境中的休眠：对称排斥

Dormancy in random environment: Symmetric exclusion

本文构建随机环境下含休眠态的两类分支随机游走，借助 Feynman–Kac 公式与扩展的抛物 Anderson 模型分析期望种群规模的长时间渐近，量化休眠对增长与生存的影响。

Equilibrium fluctuations for the slow boundary exclusion process

We prove that the equilibrium fluctuations of the symmetric simple exclusion process in contact with slow boundaries is given by an Ornstein-Uhlenbeck process with Dirichlet, Robin or Neumann boundary conditions depending on the range of the parameter that rules the slowness of the boundaries.

Hydrodynamic limit of the Symmetric Exclusion Process on a compact Riemannian manifold

We consider the symmetric exclusion process on suitable random grids that approximate a compact Riemannian manifold. We prove that a class of random walks on these random grids converge to Brownian motion on the manifold. We then consider the empirical density field of the symmetric exclusion process and prove that it converges to the solution of the heat equation on the manifold.

具有涡度的排他过程的流体动力学极限

Hydrodynamic limit of an exclusion process with vorticity

本文构造了具有伯努利乘积不变测度的不可逆排他过程，推导其扩散标度下的非对称扩散矩阵，揭示弱外场下迁移率矩阵与扩散矩阵对称部分的爱因斯坦关系，该现象在广义梯度模型中具有典型性。

Combinatorics of the Quantum Symmetric Simple Exclusion Process, associahedra and free cumulants

The Quantum Symmetric Simple Exclusion Process (QSSEP) is a model of quantum particles hopping on a finite interval and satisfying the exclusion principle. Recently Bernard and Jin have studied the fluctuations of the invariant measure for this process, when the number of sites goes to infinity. These fluctuations are encoded into polynomials, for which they have given equations and proved that these equations determine the polynomials completely. In this paper, I give an explicit combinatorial formula for these polynomials, in terms of Schröder trees. I also show that, quite surprisingly, the…

趋近零程过程的对称部分排斥过程的密度涨落场的标度极限

Scaling Limits of Density Fluctuation Fields of the Symmetric Partial Exclusion Processes Approaching the Zero Range Process

本文研究一维对称部分排斥过程（SPEP）的密度涨落场标度极限，证明其在扩散标度下收敛到与对称零程过程（SZRP）一致的随机热方程解，为SPEP近似SZRP提供严格依据。

The gradient flow approach to hydrodynamic limits for the simple exclusion process

We give a new approach to the well-known convergence to the hydrodynamic limit for the symmetric simple exclusion process (SSEP). More precisely, we characterize any possible limit of its empirical density measures as solutions to the heat equation by passing to the limit in the gradient flow structure of the particle system.

促进排除过程的平稳涨落

Stationary fluctuations for the facilitated exclusion process

本文利用FEP与零程过程的映射，推导了一维FEP在对称、弱不对称和不对称情形下的平稳涨落，并在对称情形下通过系综等价性给出了直接证明。

对称简单排斥过程平衡点的收敛速率

Rate of convergence to equilibrium of symmetric simple exclusion processes

本文给出了$\Z^d$中对称简单排它过程到平衡点的收敛速率的界。我们的结果包含了文献中已有的结果。通过统一的方法得到了更好的界和更大类的初态。该方法包括沿整个时间轨迹的n个相互作用的粒子与n个独立的粒子的演化的比较。

平衡状态下促进排斥过程的中度偏差

Moderate deviations for the facilitated exclusion process in equilibrium

本文推导了一维促进排斥过程在平稳测度下对称与非对称情形的涨落场中度偏差原理，核心是通过基于对数Sobolev不等式证明Boltzmann-Gibbs原理的超指数版本。

Steady state large deviations for one-dimensional, symmetric exclusion processes in weak contact with reservoirs

Consider the symmetric exclusion process evolving on an interval and weakly interacting at the end-points with reservoirs. Denote by $I_{[0,T]} (\cdot)$ its dynamical large deviations functional and by $V(\cdot)$ the associated quasi-potential, defined as $V(γ) = \inf_{T>0} \inf_u I_{[0,T]} (u)$, where the infimum is carried over all trajectories $u$ such that $u(0) = \barρ$, $u(T) = γ$, and $\barρ$ is the stationary density profile. We derive the partial differential equation which describes the evolution of the optimal trajectory, and deduce from this result the formula obtained by Derrida, …

Equilibrium fluctuations for diffusive symmetric exclusion with long jumps and infinitely extended reservoirs

We provide a complete description of the equilibrium fluctuations for diffusive symmetric exclusion processes with long jumps in contact with infinitely extended reservoirs and prove that they behave as generalized Ornstein-Uhlenbeck processes with various boundary conditions, depending mainly on the strength of the reservoirs. On the way, we also give a general statement about uniqueness of the Ornstein-Uhlenbeck process originated by the microscopic dynamics of the underlying interacting particle systems and adapt it to our study.

d > 1 中对称排斥过程的泊松统计、相关性消失与极值粒子极限

Poisson statistics, vanishing correlations, and extremal particle limits for symmetric exclusion in d > 1

本文研究 d≥2 维对称排斥过程在阶梯初始条件下越过边界的粒子数，证明其收敛到泊松分布，并给出极值位置的 Gumbel 极限分布。

保守随机偏微分方程与对称简单排斥过程的涨落

Conservative stochastic PDE and fluctuations of the symmetric simple exclusion process

本文提出带非线性保守噪声的 SPDE 逼近序列，刻画对称简单排斥过程在流体动力学极限附近的涨落与稀有事件，并证明零噪声大偏差速率函数一致。

Equilibrium fluctuations for the Symmetric Exclusion Process on a compact Riemannian manifold

We consider the Symmetric Exclusion Process on a compact Riemannian manifold, as introduced in van Ginkel and Redig (2020). There it was shown that the hydrodynamic limit satisfies the heat equation. In this paper we study the equilibrium fluctuations around this hydrodynamic limit. We define the fluctuation fields as functionals acting on smooth functions on the manifold and we show that they converge in distribution in the path space to a generalized Ornstein-Uhlenbeck process. This is done by proving tightness and by showing that the limiting fluctuations satisfy the corresponding martingal…

具有闭合边界的若干促进排斥过程的耦合流体动力学

Coupling hydrodynamics of several Facilitated Exclusion Processes with closed boundaries

本文通过构建映射将 Facilitated Exclusion Process 与 Simple Exclusion Process 耦合，证明了前者在对称、不对称及弱不对称机制下的流体动力学极限。

Distribution of a tagged particle position in the one-dimensional symmetric simple exclusion process with two-sided Bernoulli initial condition

For the two-sided Bernoulli initial condition with density $ρ_-$ (resp. $ρ_+$) to the left (resp. to the right), we study the distribution of a tagged particle in the one dimensional symmetric simple exclusion process. We obtain a formula for the moment generating function of the associated current in terms of a Fredholm determinant. Our arguments are based on a combination of techniques from integrable probability which have been developed recently for studying the asymmetric exclusion process and a subsequent intricate symmetric limit. An expression for the large deviation function of the ta…

嘈杂的选民排它过程

The noisy voter-exclusion process

对称排它过程和选举模型是两个相互作用的粒子系统，对于这两个系统，对偶有限粒子系统允许刻画其不变测度。在这两个过程中加上自然出生和自然死亡，仍然可以使用对偶过程来获得关于原始过程的信息。我们研究了嘈杂的选民排它过程，它通过允许所有这些相互作用的发生来概括这些过程。对偶过程被用来刻画它在各种情况下的不变测度。最后，利用耦合证明了一个相关过程的遍历定理。

非均匀介质中对称排斥过程的流体动力学极限

Hydrodynamic limit of symmetric exclusion processes in inhomogeneous media

在\cite{J} M. Jara提出了一种方法，将对称排斥过程的流体动力学极限的证明简化为均匀化问题，作为该领域最近工作的统一方法，如\cite{N}，\cite{F1}，\cite{F2}和\cite{FJL}。虽然在\cite{J}中没有说明，但在\cite{N}，\cite{F1}中已经（以不同的方式）得到了将流体动力学极限简化为均匀化问题。这两个问题之间的这种可供选择的、非常简单的关系可以追溯到K的一个概念。Nagy \cite{N}在\cite{F1} [B节]中针对$\bbZ^d$上的排除过程进行了说明，并且如\cite{F2}中所强调的，是完全通用的。上述关系式已应用于\cite{N}、\cite{F1}、\cite{F2}和\cite{FJL}，并可应用于\cite{J}中提到的其他对称排斥过程。在这个简短的说明中，我们简要回顾了完整的一般设置中的这种统一方法。最后，我们回顾一下如何均匀化问题已经解决了上述以前的作品。

Hydrodynamic behavior of long-range symmetric exclusion with a slow barrier: superdiffusive regime

We analyse the hydrodynamical behavior of the long jumps symmetric exclusion process in the presence of a slow barrier. The jump rates are given by a symmetric transition probability $p(\cdot)$ with infinite variance. When jumps occur from $\mathbb{Z}_{-}^{*}$ to $\mathbb N$ the rates are slowed down by a factor $αn^{-β}$ (with $α>0$ and $β\geq 0$). We obtain several partial differential equations given in terms of the regional fractional Laplacian on $\mathbb R^*$ and with different boundary conditions. Surprisingly, in opposition to the diffusive regime, we get different regimes depending on…

一维最近邻对称简单排斥中电流和标记粒子的大偏差

Large deviations for the current and tagged particle in 1D nearest-neighbor symmetric simple exclusion

大数定律，从某些非平衡测量开始，已经被证明是通过键的积分电流，以及一维对称最近邻简单排斥中的标记粒子[Ann. Inst. Henri Poincare Probab. Stat. 42（2006）567-577]。本文证明了相应的大偏差原理，并对速率函数进行了评价，给出了与[J. Stat. 136（2009）1-15]。