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Spatial random permutations and infinite cycles
Probability| Speaker: | Daniel Ueltschi, University of Warwick |
| Location: | 1147 MSB |
| Start time: | Wed, Apr 9 2008, 4:10PM |
Description
I will introduce the model of "spatial" random permutations. Permutations
act on a countable set of points of R^d and a weight penalizes long jumps.
The main question is about the occurrence of infinite cycles. As we will
see, infinite cycles occur for densities larger than a "critical density",
which is given by an exact expression.
I will also discuss the relation between spatial permutations and the
quantum Bose gas, and the Bose-Einstein condensation. The talk is mostly
based on the preprint arxiv/0711.1188