论文标题
TASEP的非相互作用路径构建体不均匀速率和KPZ固定点
Non-intersecting path constructions for TASEP with inhomogeneous rates and the KPZ fixed point
论文作者
论文摘要
我们考虑一个离散的时间TASEP，其中每个粒子根据伯努利随机变量以粒子依赖性和时间均匀参数跳跃。我们使用Robinson-Schensted-Knuth对应关系和某些相互交织关系的组合来表达这种相互作用的粒子系统的过渡内核，该粒子系统是根据加权，非相互作用的晶格路径的合奏，因此，作为确定点过程的边际。接下来，我们将粒子位置的联合分布表示为弗雷德尔姆决定因素，其相关内核是根据离散热方程的边界值问题给出的。解决此类问题的解决方案最终使我们以随机行走概率来表示相关内核的代表，从而将Matetski，Quastel和Remenik和Remenik（Acta Math。，2021）的制定概括为粒子和时间侵入率的情况。在完全不均匀的情况下，解决边界价值问题的解决方案的结构比同质情况更精细。
We consider a discrete-time TASEP, where each particle jumps according to Bernoulli random variables with particle-dependent and time-inhomogeneous parameters. We use the combinatorics of the Robinson-Schensted-Knuth correspondence and certain intertwining relations to express the transition kernel of this interacting particle system in terms of ensembles of weighted, non-intersecting lattice paths and, consequently, as a marginal of a determinantal point process. We next express the joint distribution of the particle positions as a Fredholm determinant, whose correlation kernel is given in terms of a boundary-value problem for a discrete heat equation. The solution to such a problem finally leads us to a representation of the correlation kernel in terms of random walk hitting probabilities, generalising the formulation of Matetski, Quastel and Remenik (Acta Math., 2021) to the case of both particle- and time-inhomogeneous rates. The solution to the boundary value problem in the fully inhomogeneous case appears with a finer structure than in the homogeneous case.
