English

Dynamic generalizations of the Asymmetric Inclusion Process, Asymmetric Brownian Energy Process and their Dualities

Probability 2025-02-19 v1 Representation Theory

Abstract

Two new interacting particle systems are introduced in this paper: dynamic versions of the asymmetric inclusion process (ASIP) and the asymmetric Brownian energy process (ABEP). Dualities and reversibility of these processes are proven, where the quantum algebra Uq(su(1,1))\mathcal{U}_q(\mathfrak{su}(1,1)) and the Al-Salam--Chihara polynomials play a crucial role. Two hierarchies of duality functions are found, where the Askey-Wilson polynomials and Jacobi polynomials sit on top.

Keywords

Cite

@article{arxiv.2502.12709,
  title  = {Dynamic generalizations of the Asymmetric Inclusion Process, Asymmetric Brownian Energy Process and their Dualities},
  author = {Carel Wagenaar},
  journal= {arXiv preprint arXiv:2502.12709},
  year   = {2025}
}