Chanal Krauth 2010
From Werner KRAUTH
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| - | '''C. Chanal, W. Krauth [http://arxiv.org/pdf/0910.1530v1 ''Convergence and coupling for spin glasses and hard spheres''] Physical Review E ''' 81''' 016705 (2010)''' | + | '''C. Chanal, W. Krauth Physical Review E ''' 81''' 016705 (2010)''' |
| + | '''Abstract: ''' We discuss convergence and coupling of Markov chains, and present general | ||
| + | relations between the transfer matrices describing these two processes. | ||
| + | We then analyze a recently developed local-patch algorithm, which | ||
| + | computes rigorous upper bound for the coupling time of a Markov chain for | ||
| + | non-trivial statistical-mechanics models. Using the "coupling from | ||
| + | the past" protocol, this allows one to exactly sample the underlying | ||
| + | equilibrium distribution. For spin glasses in two and three spatial | ||
| + | dimensions, the local-patch algorithm works at lower temperatures than | ||
| + | previous exact-sampling methods. We discuss variants of the algorithm | ||
| + | which might allow one to reach, in three dimensions, the spin-glass | ||
| + | transition temperature. The algorithm can be adapted to hard-sphere | ||
| + | models. For two-dimensional hard disks, the algorithm allows us to draw | ||
| + | exact samples at higher densities than previously possible. | ||
| + | [http://arxiv.org/pdf/0910.1530v1 Electronic version (arXiv)] | ||
| - | Long version of the Chanal Krauth (2008) paper, with | + | '''Comment''': Long version of the Chanal Krauth (2008) paper, containing an extension of the patch algorithm to hard spheres. |
| - | [http://www.phys.ens.fr/~krauth/get.php?fichier=pruning_ND.py Python implementation] of the patch algorithm | + | |
| + | [http://www.phys.ens.fr/~krauth/get.php?fichier=pruning_ND.py Python implementation of the patch algorithm] | ||
Revision as of 12:02, 29 January 2011
C. Chanal, W. Krauth Physical Review E 81 016705 (2010)
Abstract: We discuss convergence and coupling of Markov chains, and present general relations between the transfer matrices describing these two processes. We then analyze a recently developed local-patch algorithm, which computes rigorous upper bound for the coupling time of a Markov chain for non-trivial statistical-mechanics models. Using the "coupling from the past" protocol, this allows one to exactly sample the underlying equilibrium distribution. For spin glasses in two and three spatial dimensions, the local-patch algorithm works at lower temperatures than previous exact-sampling methods. We discuss variants of the algorithm which might allow one to reach, in three dimensions, the spin-glass transition temperature. The algorithm can be adapted to hard-sphere models. For two-dimensional hard disks, the algorithm allows us to draw exact samples at higher densities than previously possible.
Comment: Long version of the Chanal Krauth (2008) paper, containing an extension of the patch algorithm to hard spheres.
