Cluster expansions for hard-core systems: I introduction
Seminar Room 1, Newton Institute
CLUSTER EXPANSIONS FOR HARD-CORE SYSTEMS: I INTRODUCTION
The talk will be an introductory presentation of cluster expansions for models with self and nearest-neighbour 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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