Preprint 26/2000

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 tex2html_wrap_inline10 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 tex2html_wrap_inline12, with the distributions tex2html_wrap_inline14. We study the distribution tex2html_wrap_inline16 of the random solution at the moments tex2html_wrap_inline18. The main result is the convergence of tex2html_wrap_inline16 to an equilibrium Gaussian translation-invariant measure as tex2html_wrap_inline22. The application to the case of the Gibbs measures tex2html_wrap_inline24 with two different temperatures tex2html_wrap_inline26 is given. Limiting mean energy current density formally is tex2html_wrap_inline28 for the Gibbs measures, and it is finite tex2html_wrap_inline30 with C>0 for the convolution with a nontrivial test function.

21.02.2013, 01:40