Self-duality and shock dynamics in the n-species priority ASEP

V. Belitsky and G.M. Schütz

Stochastic Processes and their Applications, 2018, vol. 128, issue 4, 1165-1207

Abstract: We construct all invariant measures of the n-species priority asymmetric simple exclusion process with reflecting boundaries and prove reversibility. Using the symmetry of the generator of the process under the quantum algebra Uq[gl(n+1)] we derive self-duality functions. From these we obtain in explicit form the time evolution on Z of a family of measures with K shocks in terms of the transition probability of a shock exclusion process with K coloured particles with particle-dependent hopping rates and nearest-neighbour colour exchange. This process is a gas of particles that form a bound state, corresponding to shock coalescence on macroscopic scale.

Keywords: Asymmetric simple exclusion process; Duality; Quantum algebras; Shocks (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:128:y:2018:i:4:p:1165-1207

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DOI: 10.1016/j.spa.2017.07.003

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