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Cluster expansions for hard-core systems: II convergence criteria

Presented by: 
R Fernandez [Rouen]
Date: 
Wednesday 23rd January 2008 - 11:30 to 12:30
Venue: 
INI Seminar Room 1
Abstract: 

CLUSTER EXPANSIONS FOR HARD-CORE SYSTEMS: I INTRODUCTION

The talk will be an introductory presentation of cluster expansions for models with self and nearest-neighbor exclusions. It will focus on the following questions: what are cluster expansions?, what type of information they yield?, how are they used? The general abstract framework ---polymer models--- will be introduced, illustrated with a number of classical examples.

CLUSTER EXPANSIONS FOR HARD-CORE SYSTEMS: II CONVERGENCE CRITERIA

The successive convergence criteria proposed for cluster expansions will be presented and compared. The talk will include a discussion of the contrasting conceptual approaches of the different proofs, as well as numerical consequences for benchmark examples. If time permits, an alternative probabilistic scheme will also be reviewed. This scheme, which is not based on expansions, yields weaker results but does not make use of expansion methods and leads to a perfect simulation algorithm.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons