Dynamic generalizations of the Asymmetric Inclusion Process, Asymmetric Brownian Energy Process and their Dualities
Carel Wagenaar (TU Delft - Analysis)
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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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