Talagrand, Michel

Huge random structures and mean field models for spin glasses

Doc. Math. (Bielefeld) Extra Vol. ICM Berlin 1998, Vol. I, 507-536 (1998)

Summary

To explain (at least qualitatively) the unconventional magnetic behavior of certain materials, the physicists have been led to formulate and to study simple mathematical models. The concepts and methods they developed in this process appear to apply to a number of important random combinatorial optimization problems, for which they have proposed remarkable formulas. Their discoveries point towards a new branch of probability theory. Finding rigorous arguments to support their conjectures is a formidable challenge and a long range program, some steps of which are described in the present paper.

Mathematics Subject Classification

60K40, 82D30

Keywords/Phrases

random structures, mean field models for spin glasses

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