# Mathematics Colloquia and Seminars

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### Random sorting networks, permutohedron random walks, exclusion processes and sphere geodesics.

**Mathematical Physics & Probability**

Speaker: | Dan Romik, University of California at Berkeley |

Location: | 693 Kerr |

Start time: | Tue, Nov 22 2005, 3:10PM |

I will present, through conjectures, rigorous results and entertaining computer simulations, several random models for the process of sorting a list of N numbers from decreasing to increasing order by applying a sequence of nonredundant adjacent transpositions. One natural model, the Uniform Sorting Network, exhibits a surprising level of symmetry and a remarkable conjectured link to geometry. Another model, the Permutohedron Random Walk, can be solved completely by representing it as a coupled family of totally asymmetric exclusion processes. Based on joint work with Alexander Holroyd, Omer Angel, Balint Virag, Scott Sheffield and Rick Kenyon.