相关论文: One-point asymptotics for half-flat ASEP
The asymptotic pseudo-trajectory approach to stochastic approximation of Benaim, Hofbauer and Sorin is extended for asynchronous stochastic approximations with a set-valued mean field. The asynchronicity of the process is incorporated into…
In this paper, we show how a fixed point based boundary layer analysis can be used to understand phases and phase transitions in asymmetric simple exclusion processes (ASEPs) with open boundaries. In order to illustrate this method, we…
We study the asymptotic geometry of the spin foam partition function for a large class of models, including the models of Barrett and Crane, Engle, Pereira, Rovelli and Livine, and, Freidel and Krasnov. The asymptotics is taken with respect…
In previous work the authors found integral formulas for probabilities in the asymmetric simple exclusion process (ASEP) on the integer lattice. The dynamics are uniquely determined once the initial state is specified. In this note we…
We investigate the stationary distribution of asymmetric and weakly asymmetric simple exclusion processes with open boundaries. We project the stationary distribution onto a subinterval, whose size is allowed to grow with the length of the…
In non-equilibrium statistical mechanics, the Asymmetric Simple Exclusion Process (ASEP) serves as a paradigmatic example. We investigate the spectral characteristics of the ASEP, focusing on the spectral boundary of its generator matrix.…
The notion of isometric and unitary asymptotes was introduced for power bounded operators in 1989 and was generalized in 2016--2019 by K\'erchy. In particular, it was shown that there exist operators without unitary asymptote. In this paper…
We consider steady-state current activity statistics for the one-dimensional totally asymmetric simple exclusion process (TASEP). With the help of the known operator algebra (for general open boundary conditions), as well as general…
In this paper, a generalized version of dynamic ASEP is introduced, and it is shown that the process has a Markov duality property with the same process on the reversed lattice. The duality functions are multivariate $q$-Racah polynomials,…
Generalization of the one-dimensional totally asymmetric exclusion process (TASEP) with open boundary conditions in which particles are allowed to jump $l$ sites ahead with the probability $p_l\sim 1/l^{\sigma+1}$ is studied by Monte Carlo…
A condition is given, under which a general lattice point counting function is asymptotic to the corresponding ball volume growth function. This is then used to give height asymptotics in the style of the Batyrev-Manin Conjecture for…
We review recent progress in limit laws for the one-dimensional asymmetric simple exclusion process (ASEP) on the integer lattice. The limit laws are expressed in terms of a certain Painlev\'e II function. Furthermore, we take this…
In this paper, we study an exact solution of the asymmetric simple exclusion process on a periodic lattice of finite sites with two typical updates, i.e., random and parallel. Then, we find that the explicit formulas for the partition…
Using a recently developed method for proving asymptotics via orthogonal polynomial duality arXiv:2305.17602, we prove that the dynamic ASEP introduced in arXiv:1701.05239 has asymptotics which are either distributed as the Tracy--Widom…
We consider the totally asymmetric simple exclusion process (TASEP) in discrete time with sequential update. The joint distribution of the positions of selected particles is expressed as a Fredholm determinant with a kernel defining a…
We introduce a family of multi-dimensional Askey-Wilson signed measures. We offer an explicit description of the stationary measure of the open asymmetric simple exclusion process (ASEP) in the full phase diagram, in terms of integrations…
We consider the one-dimensional asymmetric simple exclusion process (ASEP) in which particles jump to the right at rate $p\in(1/2,1]$ and to the left at rate $1-p$, interacting by exclusion. In the initial state there is a finite region…
We consider an exclusion process on a periodic one-dimensional lattice where all particles perform simple symmetric exclusion at rate $1$ except for a single tracer particle, which performs partially simple asymmetric exclusion with rate…
Considering the large deviations of activity and current in the Asymmetric Simple Exclusion Process (ASEP), we show that there exists a non-trivial correspondence between the joint scaled cumulant generating functions of activity and…
In this paper, we introduce the notion of asymptotic self-similar sets on general doubling metric spaces by extending the notion of self-similar sets, and determine their Hausdorff dimensions, which gives an extension of Balogh and Rohner…