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

2025/02/18 by Wagenaar, Carel · 1 citation
#33D45 #60J60 #60J74 #FOS: Mathematics #Probability (math.PR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2502.12709

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 U_q(\mathfraksu(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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