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

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  • Belitsky, V.
  • Schütz, G.M.

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.

Suggested Citation

  • Belitsky, V. & Schütz, G.M., 2018. "Self-duality and shock dynamics in the n-species priority ASEP," Stochastic Processes and their Applications, Elsevier, vol. 128(4), pages 1165-1207.
  • Handle: RePEc:eee:spapps:v:128:y:2018:i:4:p:1165-1207
    DOI: 10.1016/j.spa.2017.07.003
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    1. Carinci, Gioia & Giardinà, Cristian & Giberti, Claudio & Redig, Frank, 2015. "Dualities in population genetics: A fresh look with new dualities," Stochastic Processes and their Applications, Elsevier, vol. 125(3), pages 941-969.
    2. Lloyd, Peter & Sudbury, Aidan & Donnelly, Peter, 1996. "Quantum operators in classical probability theory: I. "Quantum spin" techniques and the exclusion model of diffusion," Stochastic Processes and their Applications, Elsevier, vol. 61(2), pages 205-221, February.
    3. Benjamini, I. & Ferrari, P. A. & Landim, C., 1996. "Asymmetric conservative processes with random rates," Stochastic Processes and their Applications, Elsevier, vol. 61(2), pages 181-204, February.
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