Sampling the Fermi statistics and other conditional product measures

A. Gaudillière; J. Reygner

Annales de l'I.H.P. Probabilités et statistiques (2011)

  • Volume: 47, Issue: 3, page 790-812
  • ISSN: 0246-0203

Abstract

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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, illustrated in a simulation appendix and extended to (non-homogeneous) products of log-concave measures.

How to cite

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Gaudillière, A., and Reygner, J.. "Sampling the Fermi statistics and other conditional product measures." Annales de l'I.H.P. Probabilités et statistiques 47.3 (2011): 790-812. <http://eudml.org/doc/243449>.

@article{Gaudillière2011,
abstract = {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, illustrated in a simulation appendix and extended to (non-homogeneous) products of log-concave measures.},
author = {Gaudillière, A., Reygner, J.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {metropolis algorithm; Markov chain; sampling; mixing time; product measure; conservative dynamics; Metropolis algorithm},
language = {eng},
number = {3},
pages = {790-812},
publisher = {Gauthier-Villars},
title = {Sampling the Fermi statistics and other conditional product measures},
url = {http://eudml.org/doc/243449},
volume = {47},
year = {2011},
}

TY - JOUR
AU - Gaudillière, A.
AU - Reygner, J.
TI - Sampling the Fermi statistics and other conditional product measures
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2011
PB - Gauthier-Villars
VL - 47
IS - 3
SP - 790
EP - 812
AB - 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, illustrated in a simulation appendix and extended to (non-homogeneous) products of log-concave measures.
LA - eng
KW - metropolis algorithm; Markov chain; sampling; mixing time; product measure; conservative dynamics; Metropolis algorithm
UR - http://eudml.org/doc/243449
ER -

References

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