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Geometric analysis for the metropolis algorithm on Lipschitz domains

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Abstract

This paper gives geometric tools: comparison, Nash and Sobolev inequalities for pieces of the relevant Markov operators, that give useful bounds on rates of convergence for the Metropolis algorithm. As an example, we treat the random placement of N hard discs in the unit square, the original application of the Metropolis algorithm.

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Authors and Affiliations

  1. Departments of Statistics and Mathematics, Stanford University, Stanford, CA, 94305, USA

    Persi Diaconis

  2. Département de Mathématiques, Université de Nice Sophia-Antipolis, Parc Valrose, 06000, Nice Cedex 02, France

    Gilles Lebeau & Laurent Michel

Authors
  1. Persi Diaconis
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  2. Gilles Lebeau
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  3. Laurent Michel
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Corresponding author

Correspondence to Gilles Lebeau.

Additional information

P. Diaconis was supported in part by the National Science Foundation, DMS 0505673.

G. Lebeau and L. Michel were supported in part by ANR equa-disp Blan07-3-188618.

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Diaconis, P., Lebeau, G. & Michel, L. Geometric analysis for the metropolis algorithm on Lipschitz domains. Invent. math. 185, 239–281 (2011). https://doi.org/10.1007/s00222-010-0303-6

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  • DOI: https://doi.org/10.1007/s00222-010-0303-6

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