# CSM

## Seminar

### A rosetta stone: combinatorics, physics, probability

Seminar Room 1, Newton Institute

#### Abstract

The purpose of this talk is to relate enumerative combinatorics, statistical physics, and probability. Specifically, it will explain how the theory of species of structures is exactly what is needed for the equilibrium statistical mechanics of particles. Thus, for example, the condition that the rooted tree equation has a finite fixed point is precisely equivalent to the Kotecky-Preiss condition used in the theory of cluster expansions. Furthermore, there is a fixed point equation for rooted connected graphs from which the rooted tree bound follows immediately. The talk will conclude with an indication about how the recent Fernandez-Procacci cluster expansion condition corresponds to an enriched rooted tree bound. Conclusion: Combinatorics and mathematical physics tell the same story, perhaps in different languages.

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