## Electronic Journal of Probability

### Convergence of clock process in random environments and aging in Bouchaud's asymmetric trap model on the complete graph

Véronique Gayrard

#### Abstract

In this paper the celebrated arcsine aging scheme of Ben Arous and Černý is taken up. Using a brand new approach based on point processes and weak convergence techniques, this scheme is implemented in a broad class of Markov jump processes in random environments that includes Glauber dynamics of discrete disordered systems. More specifically, conditions are given for the underlying clock process (a partial sum process that measures the total time elapsed along paths of a given length) to converge to a subordinator, and consequences for certain time correlation functions are drawn. This approach is applied to Bouchaud's asymmetric trap model on the complete graph for which aging is for the first time proved, and the full, optimal picture,  obtained. Application to  spin glasses are carried out in follow up papers.

#### Article information

Source
Electron. J. Probab., Volume 17 (2012), paper no. 58, 33 pp.

Dates
Accepted: 1 August 2012
First available in Project Euclid: 4 June 2016

https://projecteuclid.org/euclid.ejp/1465062380

Digital Object Identifier
doi:10.1214/EJP.v17-2211

Mathematical Reviews number (MathSciNet)
MR2959064

Zentralblatt MATH identifier
1252.82091

Rights

#### Citation

Gayrard, Véronique. Convergence of clock process in random environments and aging in Bouchaud's asymmetric trap model on the complete graph. Electron. J. Probab. 17 (2012), paper no. 58, 33 pp. doi:10.1214/EJP.v17-2211. https://projecteuclid.org/euclid.ejp/1465062380

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