Transition between Airy_1 and Airy_2 processes and TASEP fluctuations

Simple item page
dc.creatorBorodin, Alexei
dc.creatorFerrari, Patrik L.
dc.creatorSasamoto, Tomohiro
dc.date2007-03-07
dc.date.accessioned2026-07-07T10:14:18Z
dc.date.available2026-07-07T10:14:18Z
dc.descriptionWe consider the totally asymmetric simple exclusion process, a model in the KPZ universality class. We focus on the fluctuations of particle positions starting with certain deterministic initial conditions. For large time t, one has regions with constant and linearly decreasing density. The fluctuations on these two regions are given by the Airy_1 and Airy_2 processes, whose one-point distributions are the GOE and GUE Tracy-Widom distributions of random matrix theory. In this paper we analyze the transition region between these two regimes and obtain the transition process. Its one-point distribution is a new interpolation between GOE and GUE edge distributions.
dc.description28 pages, 5 figures, LaTeX
dc.identifierhttps://arxiv.org/abs/math-ph/0703023
dc.identifierhttp://arxiv.org/abs/math-ph/0703023
dc.identifierComm. Pure Appl. Math. 61 (2008), 1603-1629
dc.identifierdoi:10.1002/cpa.20234
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/172835
dc.subjectMathematical Physics
dc.subjectStatistical Mechanics
dc.subjectProbability
dc.subject82C22, 60K35, 15A52
dc.titleTransition between Airy_1 and Airy_2 processes and TASEP fluctuations
dc.typetext

Files

Collections

arXiv