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Second class particles in the Plancherel Totally Asymmetric Simple Exclusion Process and "jeu de taquin"

Mathematical Physics & Probability

Speaker: Dan Romik, University of California, Davis
Location: 1147 MSB
Start time: Wed, Nov 30 2011, 4:10PM

The Totally Asymmetric Simple Exclusion Process, or TASEP, is a well-known system of randomly interacting particles on the integer lattice Z. When we start the system with a second-class particle at the origin and first-class particles on the negative integers, the second-class particle will choose a random speed in [-1,1] and then move asymptotically in a straight line with that speed. I will describe recent joint results with Piotr Sniady in which we proved that a similar phenomenon holds for the "Plancherel-TASEP", which is a variant of TASEP in which the probabilistic dynamics are governed by Plancherel measure, or equivalently by an application of the RSK algorithm to a sequence of i.i.d. uniform random numbers in [0,1]. In that case, the motion of the second-class particle turns out to have an equivalent description in terms of the well-known "jeu de taquin" (or "sliding game") introduced by Schutzenberger in the context of the algebraic combinatorics of Young tableaux and the representation theory of the symmetric group. The talk will also feature a surprise appearance of ideas from ergodic theory.