Probability seminar: Existence of a phase transition of the interchange process on the Hamming graph

3 February 2017, 3.40 PM - 3 February 2017, 4.40 PM

Batı Şengül, University of Bath

SM3, School of Mathematics

Batı Şengül, University of Bath

Existence of a phase transition of the interchange process on the Hamming graph

The interchange process on a finite graph is obtained by placing a particle on each vertex of the graph, then at rate 1, selecting an edge uniformly at random and swapping the two particles at either end of this edge. We consider this process on the 2-dimensional Hamming graph. The main result is a phase transition: in the subcritical phase, all of the cycles of the process have length O(log n), whereas in the supercritical phase a positive density of vertices lie in cycles of length at least n2-ε. This is joint work with Piotr Miłoś.

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Organiser: Marton Balazs

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