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The algebra describing a shock measure in the asymmetric simple exclusion model, seen from a second class particle, has finite-dimensional representations if and only if the asymmetry parameterp of the model and the left and right asymptotic densitiesp ± of the shock satisfy [(1−p)/p]r=p −(1−p +)/p +(1−p −) for some integerr≥1; the minimal dimension of the representation is then 2r. These representations can be used to calculate correlation functions in the model.
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References
B. Derrida, J. L. Lebowitz, and E. R. Speer, Shock profiles for the partially asymmetric simple exclusion process,J. Stai. Phys. 89:135–167 (1997), and references therein.
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Speer, E.R. Finite-dimensional representations of a shock algebra. J Stat Phys 89, 169–175 (1997). https://doi.org/10.1007/BF02770759
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DOI: https://doi.org/10.1007/BF02770759