Mathematics – Probability
Scientific paper
2010-08-23
Mathematics
Probability
Scientific paper
In this paper the celebrated arcsine aging scheme of G. Ben Arous and J. Cern\'y is taken up. Using a brand new approach based on point processes and weak convergence techniques, this scheme is implemented in a wide class of Markov processes that can best be described as 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 this subordinator is constructed explicitly. This approach is illustrated on Bouchaud's asymmetric trap model on the complete graph for which aging is for the first time proved, and the full, optimal picture, obtained.
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