Exceedingly Large Deviations of the Totally Asymmetric Exclusion Process

2017/08/23 by Olla, Stefano, Tsai, Li-Cheng
#60F10 (Primary) 82C22 (Secondary) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1708.07052

Abstract

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(Nt,Nξ) . 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(N²)) , referred to as speed- N² . In this work we study the speed- N² functional LDP of the TASEP, and establishes (non-matching) large deviation upper and lower bounds.

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