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

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4 Citations (Scopus)

Abstract

We compute that the growth of the occupation-time variance at the origin up to time t in dimension d = 2 with respect to asymmetric simple exclusion in equilibrium with density ρ = 1/2 is in a certain sense at least tlog (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 give a complement to bounds in the literature when d = 1, and are consistent with an important conjecture with respect to the transition function and variance of "second-class" particles.

Original languageEnglish (US)
Pages (from-to)787-802
Number of pages16
JournalJournal of Statistical Physics
Volume123
Issue number4
DOIs
StatePublished - May 2006
Externally publishedYes

Fingerprint

Asymmetric Exclusion Process
Occupation Time
exclusion
occupation
Second Class Particle
complement
Complement
estimates
Estimate

Keywords

  • Second-class particle
  • Secondary 60F05
  • Simple exclusion AMS (2000) subject classifications: Primary 60K35
  • Variance of occupation times

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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title = "Superdiffusivity of occupation-time variance in 2-dimensional asymmetric exclusion processes with density ρ = 1/2",
abstract = "We compute that the growth of the occupation-time variance at the origin up to time t in dimension d = 2 with respect to asymmetric simple exclusion in equilibrium with density ρ = 1/2 is in a certain sense at least tlog (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 give a complement to bounds in the literature when d = 1, and are consistent with an important conjecture with respect to the transition function and variance of {"}second-class{"} particles.",
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author = "Sunder Sethuraman",
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T1 - Superdiffusivity of occupation-time variance in 2-dimensional asymmetric exclusion processes with density ρ = 1/2

AU - Sethuraman, Sunder

PY - 2006/5

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N2 - We compute that the growth of the occupation-time variance at the origin up to time t in dimension d = 2 with respect to asymmetric simple exclusion in equilibrium with density ρ = 1/2 is in a certain sense at least tlog (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 give a complement to bounds in the literature when d = 1, and are consistent with an important conjecture with respect to the transition function and variance of "second-class" particles.

AB - We compute that the growth of the occupation-time variance at the origin up to time t in dimension d = 2 with respect to asymmetric simple exclusion in equilibrium with density ρ = 1/2 is in a certain sense at least tlog (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 give a complement to bounds in the literature when d = 1, and are consistent with an important conjecture with respect to the transition function and variance of "second-class" particles.

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KW - Simple exclusion AMS (2000) subject classifications: Primary 60K35

KW - Variance of occupation times

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DO - 10.1007/s10955-006-9061-7

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JF - Journal of Statistical Physics

SN - 0022-4715

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