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The Equilibrium and Non-equilibrium Statistics of su(N)-Approximations of 2d Euler Equation Driven by Thermal Noise

PDE and Applied Math Seminar

Speaker: Oleg Zaboronski, University of Warwick
Location: 2112 MSB
Start time: Thu, Apr 21 2011, 3:10PM

I will start with a review of Zeitlin's construction of finite-dimensional approximations to the two-dimensional Euler equation on the torus which preserve all conservation laws of the original Euler flow. Using techniques borrowed from random matrix theory we will analyse the stochastic dynamics of Zeitlin's truncations driven by white noise. In particular, we will see that the invariant measure is given by a Hermitean matrix model and on the approach to equilibrium the dynamics of integrals of motion is related to Dyson Brownian motions.