2002/10/31 by Gérard Ben Arous, Gerard Ben Arous, Jiri Cerny +1 · 1 citation
Business, Management and Accounting · Mathematics · Physics and Astronomy · #Advanced Queuing Theory Analysis #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics #cond-mat #math.PR #msc:60F17. #msc:60G18 #msc:60K37 #msc:82C44
paper · pdf · doi:10.1214/105051605000000124
published as Annals of Applied Probability 2005, Vol. 15, No. 2, 1161-1192 · Published at http://dx.doi.org/10.1214/105051605000000124 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2005/05/01 · arxiv created 2005/05/20 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
Let Ei be a collection of i.i.d. exponential random variables. Bouchaud’s model on ℤ is a Markov chain X(t) whose transition rates are given by wij=νexp(−β((1−a)Ei−aEj)) if i, j are neighbors in ℤ. We study the behavior of two correlation functions: ℙ[X(tw+t)=X(tw)] and ℙ[X(t')=X(tw) ∀ t'∈[tw,tw+t]]. We prove the (sub)aging behavior of these functions when β>1 and a∈[0,1].