Critical behavior for the model of random spatial permutations

Random spatial permutations arise in the study of Bose-Einstein condensates;
they are interesting as well solely from a probabilistic point of view.  With
points on the lattice, they are tractable (as is also the case for
self-avoiding walks) from a numerical approach.  We present the probability
model, the phase transition, and associated order parameters, along with
related known results and conjectures.  We focus particularly on Markov chain
Monte Carlo methods, variance estimation for correlated time series, and
finite-size scaling.

This is a dry run for a job talk; constructive feedback is welcome.

John Kerl
Mathematical Physics Seminar
September 9, 2008