On the KPZ Scaling and the KPZ Fixed Point for TASEP

IF 0.9 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2024-01-29 DOI:10.1007/s11040-024-09475-y

Yuta Arai

引用次数: 0

Abstract

We consider all totally asymmetric simple exclusion processes (TASEPs) whose transition probabilities are given by the Schütz-type formulas and which jump with homogeneous rates. We show that the multi-point distribution of particle positions and the KPZ scaling are described using the probability generating function of the rightmost particle’s jump. For all TASEPs satisfying certain assumptions, we also prove the pointwise convergence of the kernels appearing in the joint distribution of particle positions to those appearing in the KPZ fixed point formula. Our result generalizes the result of Matetski, Quastel, and Remenik [18] in the sense that we provide the KPZ fixed point formulation for a class of TASEPs, instead of for one specific TASEP.

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关于 KPZ 比例和 TASEP 的 KPZ 固定点

我们考虑了所有完全非对称简单排斥过程（TASEPs），这些过程的过渡概率由 Schütz 型公式给出，并以同质速率跃迁。我们证明，粒子位置的多点分布和 KPZ 缩放可以用最右边粒子跳跃的概率生成函数来描述。对于满足特定假设的所有 TASEP，我们还证明了粒子位置联合分布中出现的核与 KPZ 固定点公式中出现的核的点式收敛性。我们的结果概括了 Matetski、Quastel 和 Remenik [18] 的结果，即我们提供了一类 TASEP 的 KPZ 定点公式，而不是一个特定 TASEP 的 KPZ 定点公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Physics, Analysis and Geometry 数学-物理：数学物理

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas. The entire editorial board commits itself to combine the requirements of an accurate and fast refereeing process. The section on Probability and Statistical Physics focuses on probabilistic models and spatial stochastic processes arising in statistical physics. Examples include: interacting particle systems, non-equilibrium statistical mechanics, integrable probability, random graphs and percolation, critical phenomena and conformal theories. Applications of probability theory and statistical physics to other areas of mathematics, such as analysis (stochastic pde''s), random geometry, combinatorial aspects are also addressed. The section on Quantum Theory publishes research papers on developments in geometry, probability and analysis that are relevant to quantum theory. Topics that are covered in this section include: classical and algebraic quantum field theories, deformation and geometric quantisation, index theory, Lie algebras and Hopf algebras, non-commutative geometry, spectral theory for quantum systems, disordered quantum systems (Anderson localization, quantum diffusion), many-body quantum physics with applications to condensed matter theory, partial differential equations emerging from quantum theory, quantum lattice systems, topological phases of matter, equilibrium and non-equilibrium quantum statistical mechanics, multiscale analysis, rigorous renormalisation group.