On convergence to statistic equilibrium in two-temperature problem for wave equations with mixing

Tatiana V. Dudnikova, Alexander Komech, and Herbert Spohn

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Submission date: 31. Mar. 2000
Pages: 25
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Abstract:
The wave equation in the whole space is considered. The initial datum is a random function with finite mean density of the energy which also fits the mixing condition of Ibragimov-Linnik-Rosenblatt type. The random function converges to different space-homogeneous processes as , with the distributions . We study the distribution of the random solution at the moments . The main result is the convergence of to an equilibrium Gaussian translation-invariant measure as . The application to the case of the Gibbs measures with two different temperatures is given. Limiting mean energy current density formally is for the Gibbs measures, and it is finite with C>0 for the convolution with a nontrivial test function.