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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Convergence of the Wang-Landau algorithm
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by Gersende Fort, Benjamin Jourdain, Estelle Kuhn, Tony Lelièvre and Gabriel Stoltz PDF
Math. Comp. 84 (2015), 2297-2327 Request permission


We analyze the convergence properties of the Wang-Landau algorithm. This sampling method belongs to the general class of adaptive importance sampling strategies which use the free energy along a chosen reaction coordinate as a bias. Such algorithms are very helpful to enhance the sampling properties of Markov Chain Monte Carlo algorithms, when the dynamics is metastable. We prove the convergence of the Wang-Landau algorithm and an associated central limit theorem.
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Additional Information
  • Gersende Fort
  • Affiliation: LTCI, CNRS & Telecom ParisTech, 46 rue Barrault, 75634 Paris Cedex 13, France
  • Email:
  • Benjamin Jourdain
  • Affiliation: Université Paris-Est, CERMICS (ENPC), INRIA, 6-8 Avenue Blaise Pascal, F-77455 Marne-la-Vallée
  • Email:
  • Estelle Kuhn
  • Affiliation: INRA Unité MIA, Domaine de Vilvert, 78352 Jouy-en-Josas Cedex, France
  • Email:
  • Tony Lelièvre
  • Affiliation: Université Paris-Est, CERMICS (ENPC), INRIA, 6-8 Avenue Blaise Pascal, F-77455 Marne-la-Vallée
  • Email:
  • Gabriel Stoltz
  • Affiliation: Université Paris-Est, CERMICS (ENPC), INRIA, 6-8 Avenue Blaise Pascal, F-77455 Marne-la-Vallée
  • Email:
  • Received by editor(s): July 30, 2012
  • Received by editor(s) in revised form: September 26, 2013
  • Published electronically: March 23, 2015
  • Additional Notes: This work was supported by the French National Research Agency under the grants ANR-09-BLAN-0216-01 (MEGAS) and ANR-08-BLAN-0218 (BigMC)
  • © Copyright 2015 American Mathematical Society
  • Journal: Math. Comp. 84 (2015), 2297-2327
  • MSC (2010): Primary 65C05, 60J05, 82C80
  • DOI:
  • MathSciNet review: 3356027