Interacting particle systems and Hecke algebras

Oleg Zaboronski (University of Warwick)

Tuesday 8th October, 2019 16:00-17:00 Maths 311B


There are many exactly solvable interacting particle models of reaction-diffusion type in one dimension: coalescing-annihilating random walks, branching-coalescing random walks and their modifications. In each case there is a large set of duality functions, the expectations of which are straightforward to compute and which characterise the single time law of the process. Is there a single reason for the exact solvability? As it turns out the generator for each of these models can be thought of as an element of Hecke algebra. The study of representations of the latter yields the duality functions mentioned earlier. (Based on ongoing investigation by Roger Tribe and the speaker.)

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