# Mathematics Colloquia and Seminars

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### Interlaced particles in tilings and random matrices

**Mathematical Physics & Probability**

Speaker: | Eric Nordenstam, University of Vienna / MSRI |

Location: | 1147 MSB |

Start time: | Fri, Jan 27 2012, 3:10PM |

I shall show several models where interlaced particles evolve in time. One arises from the study of tilings by dominoes of a shape in the plane called the Aztec diamond. One is constructed by several Brownian motions reflecting each other. One comes from a random matrix whose elements evolve in time. For the first two, transition probabilities, respectively densities, can be written down on a nice determinantal form. The last two are determinantal processes and a kernel can be computed. If time permits I will show how to compute the inverse of the matrix whose entries are the binomial coefficients "x choose t_i-j" (where i,j=1,...,n) for indeterminate values of x and t_1,...,t_n, and how this relates to tilings.

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