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New Trends in Mathematical and Theoretical Physics
October 6, 2016 12:30, Moscow, MIAN, Gubkina, 8

On the asymptotical normality for lattice Hamiltonian dynamics. Energy transport equation

Tatiana Dudnikova

Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow
 Video records: MP4 953.5 Mb MP4 241.9 Mb

Abstract: We consider the lattice dynamics in the whole space (in the half-space) and study the Cauchy (respectively, mixed initial-boundary value) problem with random initial data. We prove the weak convergence of statistical solutions to a limit for large time. Further, we assume that the initial measure enforces slow spatial variation on the linear scale $1/\varepsilon$. We check that for times of order $1/\varepsilon$, the limit covariance changes in time and is governed by the energy transport equation.