### Abstract

Let E _{x} be a collection of i.i.d. exponential random variables. Symmetric Bouchaud's model on ℤ^{2} is a Markov chain X(t) whose transition rates are given by w _{xy} = ν exp (-βE _{x} ) if x, y are neighbours in ℤ^{2}. 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 | |

State | Published - Jan 2006 |

### Fingerprint

### Keywords

- Aging
- Lévy process
- Random walk
- Time change
- Trap model

### ASJC Scopus subject areas

- Mathematics(all)
- Statistics and Probability
- Analysis

### Cite this

*Probability Theory and Related Fields*,

*134*(1), 1-43. https://doi.org/10.1007/s00440-004-0408-1

**Aging in two-dimensional Bouchaud's model.** / Arous, Gérard Ben; Černý, Jiří; Mountford, Thomas.

Research output: Contribution to journal › Article

*Probability Theory and Related Fields*, vol. 134, no. 1, pp. 1-43. https://doi.org/10.1007/s00440-004-0408-1

}

TY - JOUR

T1 - Aging in two-dimensional Bouchaud's model

AU - Arous, Gérard Ben

AU - Černý, Jiří

AU - Mountford, Thomas

PY - 2006/1

Y1 - 2006/1

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

UR - http://www.scopus.com/inward/record.url?scp=28144439602&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=28144439602&partnerID=8YFLogxK

U2 - 10.1007/s00440-004-0408-1

DO - 10.1007/s00440-004-0408-1

M3 - Article

AN - SCOPUS:28144439602

VL - 134

SP - 1

EP - 43

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

SN - 0178-8051

IS - 1

ER -