Geometric analysis for the metropolis algorithm on Lipschitz domains

Persi Diaconis (1) , Gilles Lebeau (2) , Laurent Michel (2)

1 Department of Statistics [Stanford]
2 LJAD - Laboratoire Jean Alexandre Dieudonné

This paper gives geometric tools: comparison, Nash and Sobolev inequalities for pieces of the relevent 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 .

Domaines: Equations aux dérivées partielles [math.AP]

Persi Diaconis, Gilles Lebeau, Laurent Michel. Geometric analysis for the metropolis algorithm on Lipschitz domains. Inventiones Mathematicae, 2011, 185 (2), pp.239-281. ⟨10.1007/s00222-010-0303-6⟩. ⟨hal-01343544⟩