TASEP in half-space

2024/09/16 by Xincheng Zhang, Zhang, Xincheng
Mathematics · Decision Sciences · #Stochastic processes and statistical mechanics #Random Matrices and Applications #Probability and Risk Models

paper · pdf · doi:10.48550/arxiv.2409.09974

Abstract

In this work, we present the multi-point probability distribution of the totally asymmetric simple exclusion process (TASEP) in a half-space, starting from a general deterministic initial condition. More precisely, let h(t,x) denote the height function of TASEP at position x and time t; we provide an explicit formula for ℙ(h(t,y₁)≤ s₁, …, h(t,y_m)≤ s_m). The formula presented is well-suited for the scaling limit analysis. By applying a 1:2:3 scaling, we derive the probability distribution for the half-space KPZ fixed point, which is conjectured to be the universal process for the limit of the KPZ universality models restricted to a half-space.

Related

• On the KPZ scaling and the KPZ fixed point for TASEP
• TASEP with a general initial condition and a deterministically moving wall
• Scaling limit of the TASEP speed process
• Multi-point distribution of periodic TASEP
• Pfaffian Transition Probability and Correlation Kernel of TASEP in Half-space