For more information about this meeting, contact Mary Anne Raymond.

Title: | The oriented swap process |

Seminar: | Job Candidate Talk |

Speaker: | Dan Romik |

Abstract: |

The oriented swap process is a natural directed random walk on the symmetric
group of order N, in which we start from the identity permutation (which can
be thought of as a configuration of labeled particles), and then try to swap each pair of adjacent particles with exponential rate 1 independently of the other pairs, succeeding only if the two particles are arranged in increasing order before the swap. Eventually the process stops when it reaches the permutation (N,N-1,...,1). I will explain how to analyze the asymptotic behavior of this process as N goes to infinity (and show some amusing simulations). Using ideas from the theory of exclusion processes, one can prove results on the limiting trajectories of the particles, on the hydrodynamic limit of the system, on the rate of escape from the identity permutation and on the finishing times of individual particles. One interesting result shows that the finishing times converge in distribution after scaling to the Tracy-Widom distribution from random matrix theory. The talk is based on joint work with Omer Angel and Alexander Holroyd. |

### Room Reservation Information

Room Number: | MB114 |

Date: | 01 / 14 / 2009 |

Time: | 02:00pm - 03:00pm |