EXCEEDINGLY LARGE DEVIATIONS OF THE TOTALLY ASYMMETRIC EXCLUSION PROCESS

Stefano Olla (1) , Li-Cheng Tsai (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 Columbia University [New York]

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., hN (t, ξ) := 1 h(N t, N ξ). As hinted by the asymmetry in the upper- and lower-tail N 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(N2)), referred to as speed-N2. In this work we study the speed-N2 functional Large Deviation Principle (LDP) of the TASEP, and establish (non-matching) large deviation upper and lower bounds.

Mots clés: Corner Growth Model; Variational formula; Exclusion processes; Totally asymmetric; Large deviations

Domaines: Probabilités [math.PR]; Mécanique statistique [cond-mat.stat-mech]; Physique mathématique [math-ph]

Stefano Olla, Li-Cheng Tsai. EXCEEDINGLY LARGE DEVIATIONS OF THE TOTALLY ASYMMETRIC EXCLUSION PROCESS. Electronic Journal of Probability, 2019, 24 (16), pp.1-71. ⟨10.1214/19-EJP278⟩. ⟨hal-01577658v4⟩