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

Cédric Bernardin, Patrícia Gonçalves, Sunder Sethuraman

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

With respect to a class of long-range exclusion processes on (Formula presented.), with single particle transition rates of order (Formula presented.), starting under Bernoulli invariant measure (Formula presented.) with density (Formula presented.), 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 (Formula presented.), d and (Formula presented.) 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 (Formula presented.). However, in the asymmetric case, we study the asymptotics of the variances, which when (Formula presented.) and (Formula presented.) points to a curious dichotomy between long-range strength parameters (Formula presented.) and (Formula presented.). 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.

Original languageEnglish (US)
JournalProbability Theory and Related Fields
DOIs
StateAccepted/In press - Sep 5 2015

Fingerprint

Occupation Time
Exponent
Range of data
Scaling Limit
Class
Exclusion
Fluctuations
Additive Functionals
Exclusion Process
Hurst Parameter
Scaling
Fractional Brownian Motion
Dichotomy
Bernoulli
Invariant Measure
Upper and Lower Bounds
Space-time

Keywords

  • Additive functional
  • Exclusion
  • Exponent
  • KPZ class
  • Long-range
  • Occupation time
  • Simple

ASJC Scopus subject areas

  • Statistics and Probability
  • Analysis
  • Statistics, Probability and Uncertainty

Cite this

Occupation times of long-range exclusion and connections to KPZ class exponents. / Bernardin, Cédric; Gonçalves, Patrícia; Sethuraman, Sunder.

In: Probability Theory and Related Fields, 05.09.2015.

Research output: Contribution to journalArticle

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