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Article Dans Une Revue Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques Année : 2011

Sampling the Fermi statistics and other conditional product measures

Résumé

Through a Metropolis-like algorithm with single step computational cost of order one, we build a Markov chain that relaxes to the canonical Fermi statistics for k non-interacting particles among m energy levels. Uniformly over the temperature as well as the energy values and degeneracies of the energy levels we give an explicit upper bound with leading term km(ln k) for the mixing time of the dynamics. We obtain such construction and upper bound as a special case of a general result on (non-homogeneous) products of ultra log-concave measures (like binomial or Poisson laws) with a global constraint. As a consequence of this general result we also obtain a disorder-independent upper bound on the mixing time of a simple exclusion process on the complete graph with site disorder. This general result is based on an elementary coupling argument and extended to (non-homogeneous) products of log-concave measures.
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Dates et versions

hal-00434392 , version 1 (23-11-2009)
hal-00434392 , version 2 (18-01-2011)

Identifiants

Citer

Alexandre Gaudilliere, Julien Reygner. Sampling the Fermi statistics and other conditional product measures. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2011, 47, pp.790-812. ⟨hal-00434392v2⟩
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