Superdiffusivity of occupation-time variance in 2-dimensional asymmetric processes with density 1/2

2004/10/06 by Sunder Sethuraman, Sethuraman, Sunder
Mathematics · #60K35 #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Spectral Theory in Mathematical Physics #Stochastic processes and statistical mechanics #math.PR #msc:60K35

paper · pdf · doi:10.48550/arxiv.math/0410183

13 pages

arxiv created 2004/10/06 · openalex publication_date 2004/10/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute that the growth of the origin occupation-time variance up to time t in dimension d=2 with respect to asymmetric simple exclusion in equilibrium with density 1/2 is in a certain sense at least t(log(log t)) for general rates, and at least t(log t)^1/2 for rates which are asymmetric only in the direction of one of the axes. These estimates are consistent with conjectures with respect to the transition function and variance of 'second-class' particles.

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• An upper bound on the fluctuations of a second class particle
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