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arXiv · 2502.12709

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

Carel Wagenaar
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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 $\mathcal{U}_q(\mathfrak{su}(1,1))$ 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.

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Carel Wagenaar. 2025-02-18. Dynamic generalizations of the Asymmetric Inclusion Process, Asymmetric Brownian Energy Process and their Dualities. https://arxiv.org/abs/2502.12709

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