TASEP中第二类粒子的运动从一个渐减激波剖面开始

激波处的第二类粒子过程

The second class particle process at shocks

本文研究带原点激波间断的 TASEP，通过直接在 TASEP 中推导而非借助末次通过渗流，得到第二类粒子分布的精确恒等式、极限联合分布，并扩展一点分布结果。

TASEP on a ring in sub-relaxation time scale

Interacting particle systems in the KPZ universality class on a ring of size $L$ with $O(L)$ number of particles are expected to change from KPZ dynamics to equilibrium dynamics at the so-called relaxation time scale $t=O(L^{3/2})$. In particular the system size is expected to have little effect to the particle fluctuations in the sub-relaxation time scale $t\ll L^{3/2}$. We prove that this is indeed the case for the totally asymmetric simple exclusion process (TASEP) with two types of initial conditions. For flat initial condition, we show that the particle fluctuations are given by the Airy$…

TASEP hydrodynamics using microscopic characteristics

The convergence of the totally asymmetric simple exclusion process to the solution of the Burgers equation is a classical result. In his seminal 1981 paper, Herman Rost proved the convergence of the density fields and local equilibrium when the limiting solution of the equation is a rarefaction fan. An important tool of his proof is the subadditive ergodic theorem. We prove his results by showing how second class particles transport the rarefaction-fan solution, as characteristics do for the Burgers equation, avoiding subadditivity. In the way we show laws of large numbers for tagged particles…

双速TASEP

Two speed TASEP

我们考虑Z上的TASEP，其中两个粒子块具有不同的跳跃率。我们研究了粒子位置的大时间行为。它取决于跳跃率和我们关注的区域，我们确定了完整的过程图。特别是，我们发现了一个新的过渡过程中的区域的随机和确定性的初始条件的部分的影响相互作用。慢粒子可能会产生激波，其中粒子密度是不连续的，并且粒子位置的分布是渐近奇异的。我们在不使用第二类粒子的情况下确定了冲击波的扩散系数。我们还分析的情况下，粒子被有效地阻止了墙移动的速度等于其固有的跳跃率。

半直线开放TASEP中的第二类粒子

The second class particle in the half-line open TASEP

本研究针对半直线开放TASEP中带激波间断的两类初始条件，借助有色半空间TASEP的颜色-位置对称定理推导第二类粒子分布的精确公式，并分析其在两种标度下的渐近分布。

Statistics of TASEP with three merging characteristics

In this paper we consider the totally asymmetric simple exclusion process, with non-random initial condition having three regions of constant densities of particles. From left to right, the densities of the three regions are increasing. Consequently, there are three characteristics which meet, i.e. two shocks merge. We study the particle fluctuations at this merging point and show that they are given by a product of three (properly scaled) GOE Tracy-Widom distribution functions. We work directly in TASEP without relying on the connection to last passage percolation.

Limit law of a second class particle in TASEP with non-random initial condition

We consider the totally asymmetric simple exclusion process (TASEP) with non-random initial condition having density $ρ$ on $\mathbb{Z}_-$ and $λ$ on $\mathbb{Z}_+$, and a second class particle initially at the origin. For $ρ<λ$, there is a shock and the second class particle moves with speed $1-λ-ρ$. For large time $t$, we show that the position of the second class particle fluctuates on a $t^{1/3}$ scale and determine its limiting law. We also obtain the limiting distribution of the number of steps made by the second class particle until time $t$.

Airy_1和Airy_2过程之间的转捩和TASEP涨落

Transition between Airy_1 and Airy_2 processes and TASEP fluctuations

我们考虑完全不对称的简单排斥过程，在KPZ普适类的模型。我们专注于从某些确定性的初始条件的粒子位置的波动。对于大的时间t，有恒定的和线性下降的密度的区域。这两个区域上的涨落由Airy_1和Airy_2过程给出，其单点分布是随机矩阵理论的GOE和GUE Tracy-Widom分布。本文分析了这两个区域之间的过渡区域，得到了过渡过程。它的一点分布是GOE和GUE边缘分布之间的新插值。

TASEP with a moving wall

We consider a totally asymmetric simple exclusion on $\mathbb{Z}$ with the step initial condition, under the additional restriction that the first particle cannot cross a deterministally moving wall. We prove that such a wall may induce asymptotic fluctuation distributions of particle positions of the form $$ \mathbb{P}\Big(\sup_{τ\in \mathbb{R}}\{\textrm{Airy}_2(τ) -g(τ)\}\leq S\Big)$$ with arbitrary barrier functions $g$. This is the same class of distributions that arises as one-point asymptotic fluctuations of TASEPs with arbitrary initial conditions. Examples include Tracy-Widom GOE and G…

具有一般初始条件和确定性移动壁的TASEP

TASEP with a general initial condition and a deterministically moving wall

本文研究具有一般初始条件和确定性移动壁的TASEP，利用颜色-位置对称性将单点分布转化为阶跃初始条件TASEP的粒子位置问题，并分析了大时间渐近行为，揭示了壁影响区域边界处的新渐近现象及激波与乘积极限分布的关联。

Fluctuations of the competition interface in presence of shocks

We consider last passage percolation (LPP) models with exponentially distributed random variables, which are linked to the totally asymmetric simple exclusion process (TASEP). The competition interface for LPP was introduced and studied by Ferrari and Pimentel in [Ann. Probab. 33 (2005), 1235-1254] for cases where the corresponding exclusion process had a rarefaction fan. Here we consider situations with a shock and determine the law of the fluctuations of the competition interface around its deterministic law of large number position. We also study the multipoint distribution of the LPP aroun…

关于寿命分布类：二分马尔可夫噪声冲击模型及其假设检验应用

On classes of life distributions: Dichotomous Markov Noise Shock Model With Hypothesis Testing Applications

本文研究了二分马尔可夫噪声（DMN）驱动下的单元作为外部随机寿命递增和递减冲击的概率特性。使用DMN，我们将定义两个新的老化类的整体增加/减少（OIL/ODL）的性质在长时间的行为，这是分开的指数稳态制度。此外，对于寿命分布为整体寿命递减（ODL）类的系统，导出了一个矩不等式。我们使用这个不等式来设计一个非参数检验程序的指数对一个替代的整体递减寿命分布。