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Wednesday, April 23, 2008
10:00 AM - 11:00 AM
CNLS Conference Room (TA-3, Bldg 1690)


Random walk of hard particles and integrable systems

Aleksander Orlov
Nonlinear Studies Laboratory, Oceanology Institute, Moscow

We consider a lattice gas model describing random hops of particles, which was suggested by M. E. Fisher. We find connection of this model to classical integrable systems. We have established that the tau function - the central object in integrability - on the one hand generates transition probabilities between configurations of the hard particles, and, on the other hand, generates "partition functions" for this random model. After finding long time asymptotics, we identify a phase transition w.r.t. a hopping rate of the particles. (A joint work with J. Harnad and J. van de Leur.)

Host: Misha Chertkov, T-13