## Jakob Björnberg (01/04/16)

Math Colloquium

### Speaker: Jakob Björnberg

Title: Random permutations and quantum Heisenberg models

Location: V-157, VRII.

Time: Friday, April 1 at 13:20.

### Abstract:

The interchange process (or random-transposition random walk) is a model for random permutations which is closely related to a model from quantum statistical physics (the ferromagnetic Heisenberg model). In fact, certain ‘cycle-weighted’ interchange processes are equivalent to the latter, and in this talk we present results on such processes. Magnetic ordering in the physical model translates to the occurrence of large cycles in the random permutation.

We focus on the case when the underlying graph is the complete graph (i.e. the ‘mean-field’ case in physical jargon). By a combination of probabilistic techniques and some group character theory we can obtain nice formulas for expectation values in the model, and then use these to identify the critical point.