Aging in two-dimensional Bouchaud's model

Gérard Ben Arous; Jiří Černý; Thomas Mountford

doi:10.1007/s00440-004-0408-1

Aging in two-dimensional Bouchaud's model

Gérard Ben Arous, Jiří Černý, Thomas Mountford

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let E _x be a collection of i.i.d. exponential random variables. Symmetric Bouchaud's model on ℤ² is a Markov chain X(t) whose transition rates are given by w _xy = ν exp (-βE _x ) if x, y are neighbours in ℤ². We study the behaviour of two correlation functions: ℙ[X(t _w +t) = X(t _w )] and ℙ[X(t') = X(t _w ) ∀ t' [t_w , t_w + t]]. We prove the (sub)aging behaviour of these functions when β > 1.

Original language	English (US)
Pages (from-to)	1-43
Number of pages	43
Journal	Probability Theory and Related Fields
Volume	134
Issue number	1
DOIs	https://doi.org/10.1007/s00440-004-0408-1
State	Published - Jan 2006

Keywords

Aging
Lévy process
Random walk
Time change
Trap model

ASJC Scopus subject areas

Analysis
Statistics and Probability
Statistics, Probability and Uncertainty

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10.1007/s00440-004-0408-1

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abstract = "Let E x be a collection of i.i.d. exponential random variables. Symmetric Bouchaud's model on ℤ2 is a Markov chain X(t) whose transition rates are given by w xy = ν exp (-βE x ) if x, y are neighbours in ℤ2. We study the behaviour of two correlation functions: ℙ[X(t w +t) = X(t w )] and ℙ[X(t') = X(t w ) ∀ t' [tw , tw + t]]. We prove the (sub)aging behaviour of these functions when β > 1.",

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AU - Arous, Gérard Ben

AU - Černý, Jiří

AU - Mountford, Thomas

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N2 - Let E x be a collection of i.i.d. exponential random variables. Symmetric Bouchaud's model on ℤ2 is a Markov chain X(t) whose transition rates are given by w xy = ν exp (-βE x ) if x, y are neighbours in ℤ2. We study the behaviour of two correlation functions: ℙ[X(t w +t) = X(t w )] and ℙ[X(t') = X(t w ) ∀ t' [tw , tw + t]]. We prove the (sub)aging behaviour of these functions when β > 1.

AB - Let E x be a collection of i.i.d. exponential random variables. Symmetric Bouchaud's model on ℤ2 is a Markov chain X(t) whose transition rates are given by w xy = ν exp (-βE x ) if x, y are neighbours in ℤ2. We study the behaviour of two correlation functions: ℙ[X(t w +t) = X(t w )] and ℙ[X(t') = X(t w ) ∀ t' [tw , tw + t]]. We prove the (sub)aging behaviour of these functions when β > 1.

KW - Aging

KW - Lévy process

KW - Random walk

KW - Time change

KW - Trap model

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Aging in two-dimensional Bouchaud's model

Abstract

Keywords

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