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The dynamic phi^4 model in the plane

Presented by: 
J-C Mourrat ENS - Lyon
Date: 
Thursday 5th February 2015 - 16:00 to 17:00
Venue: 
INI Seminar Room 2
Abstract: 
The dynamic phi^4 model is a non-linear stochastic PDE which involves a cubic power of the solution. In dimensions 3 and less, solutions are expected to have the same local regularity as the linearised equation, for which the law of the Gaussian free field is invariant. Hence, in dimensions 2 and 3, some renormalisation needs to be performed in order to define the cubic power of the solution. In the (full) plane, I will explain how to do this and show that the stochastic PDE has a well-defined solution for all times. If time permits, I will also sketch a proof that the model is the scaling limit of a near-critical Ising model with long-range interactions. Joint work with Hendrik Weber.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons