Occupation times of long-range exclusion and connections to KPZ class exponents

• 成果类型: Article
• 署名作者: Bernardin, Cedric; Goncalves, Patricia; Sethuraman, Sunder
• 署名单位: Universite Cote d'Azur; Centre National de la Recherche Scientifique (CNRS); Universidade do Minho; University of Arizona
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-015-0661-5
• 发表日期: 2016
• 页码: 365-428
• 关键词: CENTRAL-LIMIT-THEOREM; additive-functionals; tagged particle; fluctuations; superdiffusivity; diffusion; systems; equilibrium; variance; site

摘要

With respect to a class of long-range exclusion processes on , with single particle transition rates of order , starting under Bernoulli invariant measure with density , we consider the fluctuation behavior of occupation times at a vertex and more general additive functionals. Part of our motivation is to investigate the dependence on , d and with respect to the variance of these functionals and associated scaling limits. In the case the rates are symmetric, among other results, we find the scaling limits exhaust a range of fractional Brownian motions with Hurst parameter . However, in the asymmetric case, we study the asymptotics of the variances, which when and points to a curious dichotomy between long-range strength parameters and . In the former case, the order of the occupation time variance is the same as under the process with symmetrized transition rates, which are calculated exactly. In the latter situation, we provide consistent lower and upper bounds and other motivations that this variance order is the same as under the asymmetric short-range model, which is connected to KPZ class scalings of the space-time bulk mass density fluctuations.