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Busemann functions and the speed of a second class particle in the rarefaction fan. (English) Zbl 1276.60108

Summary: We show how the results in [the authors, Probab. Theory Relat. Fields 154, No. 1–2, 89–125 (2012; Zbl 1262.60094)], about the Busemann functions in last-passage percolation, can be used to calculate the asymptotic distribution of the speed of a single second class particle starting from an arbitrary deterministic configuration which has a rarefaction fan, in either the totally asymmetric exclusion process or the Hammersley interacting particle process. The method is to use the well-known last-passage percolation description of the exclusion process and of the Hammersley process, and then the well-known connection between second class particles and competition interfaces.

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
82C21 Dynamic continuum models (systems of particles, etc.) in time-dependent statistical mechanics

Citations:

Zbl 1262.60094
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References:

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