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

Carel Wagenaar

doi:10.1007/s10955-026-03575-5

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

Carel Wagenaar^*

^*Corresponding author for this work

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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)) 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.

Original language	English
Article number	13
Number of pages	61
Journal	Journal of Statistical Physics
Volume	193
Issue number	2
DOIs	https://doi.org/10.1007/s10955-026-03575-5
Publication status	Published - 2026

Keywords

Diffusion Process
Inclusion Process
Markov Duality
Orthogonal Polynomials

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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)) 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.",

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KW - Diffusion Process

KW - Inclusion Process

KW - Markov Duality

KW - Orthogonal Polynomials

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

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Keywords

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