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

Author(s)

Belitsky, V. ^[1] ; Schuetz, G. M. ^{[2, 3]}

Affiliation

^[1] Univ Sao Paulo, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Sao Paulo, SP - Brazil

^[2] Forschungszentrum Julich, Inst Complex Syst 2, D-52425 Julich - Germany

^[3] Univ Bonn, Interdisziplinares Zentrum Komplexe Syst, Bruhler Str 7, D-53119 Bonn - Germany

• Document type: Journal article
• Source: Stochastic Processes and their Applications; v. 128, n. 4, p. 1165-1207, APR 2018.
• Web of Science Citations: 2

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 U-q{[}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. (C) 2017 Elsevier B.V. All rights reserved. (AU)

• FAPESP's process: 15/15258-9 - Duality and shock measures in stochastic interacting particle systems
• Grantee: Vladimir Belitsky
• Support Opportunities: Research Grants - Visiting Researcher Grant - International