A Fredholm Determinant Representation in ASEP

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dc.creatorTracy, Craig A.
dc.creatorWidom, Harold
dc.date2008-04-09
dc.date2008-04-25
dc.date.accessioned2026-07-07T09:46:47Z
dc.date.available2026-07-07T09:46:47Z
dc.descriptionIn previous work the authors found integral formulas for probabilities in the asymmetric simple exclusion process (ASEP) on the integer lattice. The dynamics are uniquely determined once the initial state is specified. In this note we restrict our attention to the case of step initial condition with particles at the positive integers, and consider the distribution function for the m'th particle from the left. In the previous work an infinite series of multiple integrals was derived for this distribution. In this note we show that the series can be summed to give a single integral whose integrand involves a Fredholm determinant. We use this determinant representation to derive (non-rigorously, at this writing) a scaling limit.
dc.description12 Pages. Version 3 includes a scaling conjecture
dc.identifierhttps://arxiv.org/abs/0804.1379
dc.identifierhttp://arxiv.org/abs/0804.1379
dc.identifierJournal of Statistical Physics 132 (2008), 291-300.
dc.identifierdoi:10.1007/s10955-008-9562-7
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/163652
dc.subjectProbability
dc.subjectMathematical Physics
dc.subject60K35
dc.titleA Fredholm Determinant Representation in ASEP
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