连续介质中无限粒子系统的正交交织算子

Intertwining and Duality for Consistent Markov Processes

In this paper we derive intertwining relations for a broad class of conservative particle systems both in discrete and continuous setting. Using the language of point process theory, we are able to derive a natural framework in which duality and intertwining can be formulated. We prove falling factorial and orthogonal polynomial intertwining relations in a general setting. These intertwinings unite the previously found classical and orthogonal self-dualities in the context of discrete particle systems and provide new dualities for several interacting systems in the continuum. We also introduce…

连续粒子系统的交织：一种代数方法

Intertwinings for Continuum Particle Systems: an Algebraic Approach

本文在一般空间粒子系统中发展了基于 $\mathfrak{su}(1,1)$ 流代数的交织代数方法，构造了酉算子作为 Markov 过程的自交织子，并建立了与离散情形相对应的连续结果。

Orthogonal Polynomial Stochastic Duality Functions for Multi-Species SEP$(2j)$ and Multi-Species IRW

We obtain orthogonal polynomial self-duality functions for multi-species version of the symmetric exclusion process (SEP$(2j)$) and the independent random walker process (IRW) on a finite undirected graph. In each process, we have $n>1$ species of particles. In addition, we allow up to $2j$ particles to occupy each site in the multi-species SEP$(2j)$. The duality functions for the multi-species SEP$(2j)$ and the multi-species IRW come from unitary intertwiners between different $*$-representations of the special linear Lie algebra $\mathfrak{sl}_{n+1}$ and the Heisenberg Lie algebra $\mathfrak…

广义动态不对称排斥过程：正交对偶性与退化

A Generalized Dynamic Asymmetric Exclusion Process: Orthogonal Dualities and Degenerations

本文引入了动态 ASEP 的广义版本，利用量子代数表示理论构建其生成元，证明了其基于多元 $q$-Racah 多项式的 Markov 对偶性，并通过极限推导出其他粒子系统的对偶性。