# Mathematics Colloquia and Seminars

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### Searching for the Tracy-Widom distribution in nonequilibrium processes

**Mathematical Physics & Probability**

Speaker: | Christian Mendl, Stanford University |

Related Webpage: | http://christian.mendl.net/ |

Location: | 1147 MSB |

Start time: | Wed, Oct 19 2016, 4:30PM |

While originally discovered in the context of the Gaussian unitary ensemble, the Tracy-Widom distribution also rules the height fluctuations of growth processes. This suggests that there might be other nonequilibrium processes in which the Tracy-Widom distribution plays an important role. In the talk we study one-dimensional systems with domain wall initial conditions. For an appropriate choice of parameters, the profile develops a rarefaction wave while maintaining the initial equilibrium states far to the left and right, which thus serve as infinitely extended thermal reservoirs. For a Fermi-Pasta-Ulam type anharmonic chain, we will demonstrate that the time-integrated current has a deterministic contribution, linear in time t, and fluctuations of size t^{1/3} with a Tracy-Widom distributed random amplitude.

References:Phys. Rev. E 93, 060101(R) (2016), arXiv:1512.06292