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Infinitely many non-intersecting random walks

Mathematical Physics & Probability

Speaker: Vadim Gorin, MSRI (Berkeley) and IITP (Moscow)
Location: 1147 MSB
Start time: Wed, Feb 1 2012, 4:10PM

Given N independent one-dimensional random walks (subject to certain technical conditions) it is not hard to condition them never to collide. The resulting conditional process will be both a Markov chain and a determinantal point process. These chains turn out to be related to random matrices and random tilings. In the talk we are going to discuss what happens in the limit when N tends to infinity. The key idea for the construction of the limit object is to link the above Markov chains for various values of N. As we will see, the limit Markov process is also closely related to TASEP with particle-dependent jump rates. The talk is based on joint work with Alexei Borodin.