Pantheon SEMPARIS Le serveur des sťminaires parisiens Paris

Status Confirmed
Seminar Series IPHT-PHM
Subjects math-ph
Date Monday 7 October 2019
Time 11:00
Institute IPHT
Seminar Room Salle Claude Itzykson, B‚t. 774
Speaker's Last Name Alexander M. Povolotsky
Speaker's First Name
Speaker's Email Address
Speaker's Institution Joint Institute for Nuclear Research, Dubna
Title Statistics of Avalanche Currents in the Raise and Peel model
Abstract The Raise and Peel model is a stochastic model of fluctuating interface with non-local avalanche dynamics. Its dynamical rules stem from the  structure of a specific representation of the Temperley-Lieb algebra, and its stochastic generator can be represented by the Hamiltonian of the XXZ Heisenberg quantum spin chain with twisted boundary conditions.  We describe the  recent progress  in description of the statistics of the avalanches in the model. We focus on the large deviations of two avalanche currents in the thermodynamic limit,  which reveal a  phase transition in the behaviour of one current conditioned to  atypical values of another one. We  also describe a proof of the  laws of  large numbers for the two currents at arbitrary finite lattices, which in addition proves two earlier conjectures on the structure of the stationary state of the model. The technique is based on the analysis of the largest eigenvalue of the deformed stochastic generator using the Bethe ansatz and Baxter
arXiv Preprint Number

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