Date:
Sun, 04/06/201711:00-13:00
Location:
Ross 63 (NOTE THE UNUSUAL LOCATION)
Speaker: Gil Alon, Open University
Title: On cards and magnets
Abstract:
The interchange process is a random walk on the symmetric group, where the steps are multiplications by transpositions, drawn according to a distribution encoded in a weighted graph. It is a nice meeting point of probability, representation theory, and physics. We will describe some of these connections, starting with our previous work on large cycles of a permutation in the process. Then we will describe the connection to a physical model (the Heisenberg quantum ferromagnet), discovered by Balint Toth, and a related conjecture of Toth on the interchange process. We will show the (so called) mean-field case of Toth's conjecture: The case where the underlying graph is the complete graph with equal weights.
Joint work with Gady Kozma.
Title: On cards and magnets
Abstract:
The interchange process is a random walk on the symmetric group, where the steps are multiplications by transpositions, drawn according to a distribution encoded in a weighted graph. It is a nice meeting point of probability, representation theory, and physics. We will describe some of these connections, starting with our previous work on large cycles of a permutation in the process. Then we will describe the connection to a physical model (the Heisenberg quantum ferromagnet), discovered by Balint Toth, and a related conjecture of Toth on the interchange process. We will show the (so called) mean-field case of Toth's conjecture: The case where the underlying graph is the complete graph with equal weights.
Joint work with Gady Kozma.