### Generalised Gibbs Measures for the Classical Toda Lattice

Probability Seminar

11th December 2020, 3:00 pm – 4:00 pm

, online

According to statistical mechanics, Gibbs measures for a many-particle

system are constructed from number, momentum, and energy, which are

believed to be generically the only locally conserved fields. The

classical Toda lattice is an integrable system and thus possesses a

countable list of local conservation laws. Accordingly Gibbs measures

of the Toda chain are indexed by an infinite set of parameters, rather

than only three. This is the meaning of “generalised" in the title.

Specifically for the Toda lattice, we will discuss the structure of

generalised Gibbs measures and point out the connection to the

one-dimensional log gas. This information is a central building block

when writing down the appropriate Euler type equations for the Toda

lattice.

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