# Mathematics Colloquia and Seminars

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### The Stationary Distribution for Totally Asymmetric Multispecies Exclusion Processes

**Mathematical Physics & Probability**

Speaker: | Arvind Ayyer, UC Davis |

Location: | 1147 MSB |

Start time: | Wed, May 18 2011, 4:10PM |

The totally asymmetric simple exclusion process (TASEP) on a periodic lattice is of interest in statistical mechanics as possibly the simplest nonequilibrium (irreversible) process. There has been considerable work generalizing the process to include multiple species of particles. The stationary state of the system is then given in terms of the "matrix ansatz". There is also a beautiful probabilistic description due to Ferrari and Martin in terms of queueing processes. I will review previous work and end with a new construction of the stationary state of the TASEP with N species of particles on a ring of L sites in terms of the Markov chain with N-1 species of particles. This work is joint with C. Arita, S. Prolhac and K. Mallick.