Electronic Journal of Probability

Exceedingly large deviations of the totally asymmetric exclusion process

Stefano Olla and Li-Cheng Tsai

Full-text: Open access

Abstract

Consider the Totally Asymmetric Simple Exclusion Process (TASEP) on the integer lattice $ \mathbb{Z} $. We study the functional Large Deviations of the integrated current $ \mathsf{h} (t,x) $ under the hyperbolic scaling of space and time by $ N $, i.e., $ \mathsf{h} _{N}(t,\xi ) := \frac{1} {N}\mathsf{h} (Nt,N\xi ) $. 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 $. In this work we study the speed-$ N^2 $ functional Large Deviation Principle (LDP) of the TASEP, and establish (non-matching) large deviation upper and lower bounds.

Article information

Source
Electron. J. Probab., Volume 24 (2019), paper no. 16, 71 pp.

Dates
Received: 29 June 2018
Accepted: 9 February 2019
First available in Project Euclid: 22 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1550826099

Digital Object Identifier
doi:10.1214/19-EJP278

Subjects
Primary: 60F10: Large deviations
Secondary: 82C22: Interacting particle systems [See also 60K35]

Keywords
large deviations exclusion processes totally asymmetric corner growth model variational formula

Rights
Creative Commons Attribution 4.0 International License.

Citation

Olla, Stefano; Tsai, Li-Cheng. Exceedingly large deviations of the totally asymmetric exclusion process. Electron. J. Probab. 24 (2019), paper no. 16, 71 pp. doi:10.1214/19-EJP278. https://projecteuclid.org/euclid.ejp/1550826099


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