Exceedingly Large Deviations of the Totally Asymmetric Exclusion Process
Olla, Stefano; Tsai, Li-Cheng (2017), Exceedingly Large Deviations of the Totally Asymmetric Exclusion Process, Electronic Journal of Probability, Institute of Mathematical Statistics (IMS). 10.1214/19-EJP278
TypeArticle accepté pour publication ou publié
Journal nameElectronic Journal of Probability, Institute of Mathematical Statistics (IMS)
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CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)Consider the Totally Asymmetric Simple Exclusion Process (TASEP) on the integer lattice Z. We study the functional Large Deviations of the integrated current h(t, x) under the hyperbolic scaling of space and time by N , i.e., h N (t, ξ) := 1 N h(N t, N ξ). As hinted by the asymmetry in the upper-and lower-tail large deviations of the exponential Last Passage Percolation, the TASEP exhibits two types of deviations. One type of deviations occur with probability exp(−O(N)), referred to as speed-N ; while the other with probability exp(−O(N 2)), referred to as speed-N 2. In this work we prove the speed-N 2 functional Large Deviation Principle (LDP) of the TASEP, with an explicit rate function. Our result complements the speed-N LDP studied in Jensen [Jen00] and Varadhan [Var04]. Also, viewing the TASEP as a degeneration of the stochastic Six Vertex Model, we interpret our result as giving an explicit formula of the surface tension function of a toy-version titling model.
Subjects / Keywordsmathématiques; probabilités; physique; matière condensée; mécanique statistique; physique mathématique
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