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2012 Convergence of clock process in random environments and aging in Bouchaud's asymmetric trap model on the complete graph
Véronique Gayrard
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Electron. J. Probab. 17: 1-33 (2012). DOI: 10.1214/EJP.v17-2211

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.

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Véronique Gayrard. "Convergence of clock process in random environments and aging in Bouchaud's asymmetric trap model on the complete graph." Electron. J. Probab. 17 1 - 33, 2012. https://doi.org/10.1214/EJP.v17-2211

Information

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

zbMATH: 1252.82091
MathSciNet: MR2959064
Digital Object Identifier: 10.1214/EJP.v17-2211

Subjects:
Primary: 82C44
Secondary: 60F17, 60K35, 82D30

JOURNAL ARTICLE
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