Extremal Reversible Measures for the Exclusion Process

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。

Universality of cutoff for exclusion with reservoirs

We consider the reversible exclusion process with reservoirs on arbitrary networks. We characterize the spectral gap, mixing time, and mixing window of the process, in terms of certain simple statistics of the underlying network. Among other consequences, we establish a non-conservative analogue of Aldous's spectral gap conjecture, and we show that cutoff occurs if and only if the product condition is satisfied. We illustrate this by providing explicit cutoffs on discrete lattices of arbitrary dimensions and boundary conditions, which substantially generalize recent one-dimensional results. We…

Couplings and attractiveness for general exclusion processes

Attractiveness is a fundamental tool to study interacting particle systems and the basic coupling construction is a usual route to prove this property, as for instance in the simple exclusion process. We consider here general exclusion processes where jump rates from an occupied site to an empty one depend not only on the location of the jump but also possibly on the whole configuration. These processes include in particular exclusion processes with speed change introduced by F. Spitzer in [18]. For such processes we derive necessary and sufficient conditions for attractiveness, through the co…

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。

One dimensional nearest neighbor exclusion processes in inhomogeneous and random environments

The processes described in the title always have reversible stationary distributions. In this paper, we give sufficient conditions for the existence of, and for the nonexistence of, nonreversible stationary distributions. In the case of an i.i.d. environment, these combine to give a necessary and sufficient condition for the existence of nonreversible stationary distributions.

Self-Duality for the Two-Component Asymmetric Simple Exclusion Process

We study a two-component asymmetric simple exclusion process (ASEP) that is equivalent to the ASEP with second-class particles. We prove self-duality with respect to a family of duality functions which are shown to arise from the reversible measures of the process and the symmetry of the generator under the quantum algebra $U_q[\mathfrak{gl}_3]$. We construct all invariant measures in explicit form and discuss some of their properties. We also prove a sum rule for the duality functions.

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…

Exclusion processes in higher dimensions: Stationary measures and convergence

There has been significant progress recently in our understanding of the stationary measures of the exclusion process on $Z$. The corresponding situation in higher dimensions remains largely a mystery. In this paper we give necessary and sufficient conditions for a product measure to be stationary for the exclusion process on an arbitrary set, and apply this result to find examples on $Z^d$ and on homogeneous trees in which product measures are stationary even when they are neither homogeneous nor reversible. We then begin the task of narrowing down the possibilities for existence of other sta…

开放相互作用粒子系统与伊辛测度

Open interacting particle systems and Ising measures

本文提出了一种扩展晶格气体模型的开放边界不对称排斥过程，证明了一维伊辛测度的不变性，并推测了由边界诱导相变的相图，揭示了两种极值电流相的存在。

排斥过程上随机游走弹道性的尖锐阈值

Sharp threshold for the ballisticity of the random walk on the exclusion process

本文研究排斥过程平流下随机游走的弹道性，证明回溯概率在临界密度处发生尖锐转变，速度严格单调且零速度区域坍缩为单点，从而解决一个已有猜想。

广义动态不对称排斥过程：正交对偶性与退化

A Generalized Dynamic Asymmetric Exclusion Process: Orthogonal Dualities and Degenerations

本文引入了动态 ASEP 的广义版本，利用量子代数表示理论构建其生成元，证明了其基于多元 $q$-Racah 多项式的 Markov 对偶性，并通过极限推导出其他粒子系统的对偶性。

多车道排他过程的不变测度

Invariant measures for multilane exclusion process

本文研究了双车道水平梯子上的简单排他过程，证明了其极值不变测度集合由乘积 Bernoulli 测度和至多三种激波测度构成，并在特定参数下完全确定了该集合，推广了现有理论。

保守动力学趋向平衡的松弛 II：非梯度排斥过程

Relaxation to equilibrium of conservative dynamics II: non-gradient exclusion processes

针对可逆速度交换排斥过程，证明其半群满足显式常数方差衰减，将已有结果推广至非梯度模型，结合正则化、混沌展开与均匀化理论。

$K$-对称排斥过程中极值的点过程收敛性

Point process convergence of extremes in $K$-symmetric exclusion

本文研究$K$-对称排斥过程的极端粒子，证明其顺序统计量经超扩散标度后收敛为指数强度Poisson随机测度，并推广到截断构型与任意$K\geq2$。

Stationary States of the One-Dimensional Discrete-Time Facilitated Symmetric Exclusion Process

We describe the extremal translation invariant stationary (ETIS) states of the facilitated exclusion process on $\mathbb{Z}$. In this model all particles on sites with one occupied and one empty neighbor jump at each integer time to the empty neighbor site, and if two particles attempt to jump into the same empty site we choose one randomly to succeed. The ETIS states are qualitatively different for densities $ρ<1/2$, $ρ=1/2$, and $1/2<ρ<1$, but in each density region we find states which may be grouped into families, each of which is in natural correspondence with the set of all ergodic measu…

Coupling, Attractiveness and Hydrodynamics for Conservative Particle Systems

Attractiveness is a fundamental tool to study interacting particle systems and the basic coupling construction is a usual route to prove this property, as for instance in simple exclusion. The derived Markovian coupled process $(ξ_t,ζ_t)_{t\geq 0}$ satisfies: (A) if $ξ_0\leqζ_0$ (coordinate-wise), then for all $t\geq 0$, $ξ_t\leqζ_t$ a.s. In this paper, we consider generalized misanthrope models which are conservative particle systems on $\Z^d$ such that, in each transition, $k$ particles may jump from a site $x$ to another site $y$, with $k\geq 1$. These models include simple exclusion for wh…

The impulse cutoff an entropy functional measure on trajectories of Markov diffusion process integrating in information path functional

The impulses, cutting entropy functional (EF) measure on trajectories Markov diffusion process, integrate information path functional (IPF) composing discrete information Bits extracted from observing random process. Each cut brings memory of the cutting entropy, which provides both reduction of the process entropy and discrete unit of the cutting entropy a Bit. Consequently, information is memorized entropy cutting in random observations which process interactions. The origin of information associates with anatomy creation of impulse enables both cut entropy and stipulate random process gener…