On a Two-Temperature Problem for Wave Equation

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dc.creatorDudnikova, T. V.
dc.creatorKomech, A. I.
dc.creatorSpohn, H.
dc.date2005-08-22
dc.date.accessioned2026-07-07T04:32:17Z
dc.date.available2026-07-07T04:32:17Z
dc.descriptionConsider the wave equation with constant or variable coefficients in $\R^3$. The initial datum is a random function with a finite mean density of energy that also satisfies a Rosenblatt- or Ibragimov-Linnik-type mixing condition. The random function converges to different space-homogeneous processes as $x_3\to\pm\infty$, with the distributions $μ_\pm$. We study the distribution $μ_t$ of the random solution at a time $t\in\R$. The main result is the convergence of $μ_t$ to a Gaussian translation-invariant measure as $t\to\infty$ that means central limit theorem for the wave equation. The proof is based on the Bernstein `room-corridor' argument. The application to the case of the Gibbs measures $μ_\pm=g_\pm$ with two different temperatures $T_{\pm}$ is given. Limiting mean energy current density formally is $-\infty\cdot (0,0,T_+ -T_-)$ for the Gibbs measures, and it is finite and equals to $-C(0,0,T_+ -T_-)$ with $C>0$ for the convolution with a nontrivial test function.
dc.description30 pages
dc.identifierhttps://arxiv.org/abs/math-ph/0508044
dc.identifierhttp://arxiv.org/abs/math-ph/0508044
dc.identifierMarkov Processes and Related Fields 8 (2002), no.1, 43-80
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58133
dc.subjectMathematical Physics
dc.subjectProbability
dc.subject60Fxx, 60Gxx, 82-xx
dc.titleOn a Two-Temperature Problem for Wave Equation
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