arXiv subjects

Kazushige Endo

Publications and source records attributed to Kazushige Endo.

4 recordsLinked to original sources

arXiv2026

Stationary Measures and Mean Flux Depending on Multiple Conserved Quantities in a Stochastic Cellular Automaton

We analyze a stochastic 5-neighbor cellular automaton with several conserved quantities, including the particle density. By examining the eigenvalue problem of the associated transition matrix, we derive an explicit formula for the stationary distribution on each irreducible component, in which the weight of each configuration is expressed in terms of the numbers of occurrences of two specific local patterns. This analysis further allows us to theoretically derive the dependence of the mean flux on the conserved quantities. In particular, we recover the mean flux formula in the deterministic case by taking the zero-noise limit of the system.

math-ph↗

arXiv2022

Asymptotic behavior of a stochastic particle system of 5 neighbors

We analyze a stochastic particle system of 5 neighbors. Considering eigenvalue problem of transition matrix, we propose a conjecture that asymptotic distribution of the system is determined by the number of specific local patterns in the asymptotic solution. Based on the conjecture, mean flux which depends of a pair of the conserved quantities is derived theoretically. Moreover, we obtain mean flux in the deterministic case through the limit of stochastic parameter.

math-ph↗

arXiv2021

Three-dimensional fundamental diagram of particle system of 5 neighbors with two conserved densities

We discuss a particle system of 5 neighbors with two independent conserved densities. The mean momentum uniquely depends on a pair of the densities and a three-dimensional fundamental diagram is obtained. It shows the phase transition of behavior of asymptotic solution to the system. Moreover, we propose two other systems which have the similar unique dependency obtained numerically.

math-ph↗

arXiv2019

Evaluation on asymptotic distribution of particle systems expressed by probabilistic cellular automata

We propose some conjectures for asymptotic distribution of probabilistic Burgers cellular automaton (PBCA) which is defined by a simple motion rule of particles including a probabilistic parameter. Asymptotic distribution of configurations converges to a unique steady state for PBCA. We assume some conjecture on the distribution and derive the asymptotic probability expressed by GKZ hypergeometric function. If we take a limit of space size to infinity, a relation between density and flux of particles for infinite space size can be evaluated. Moreover, we propose two extended systems of PBCA of which asymptotic behavior can be analyzed as PBCA.

math-ph↗