On Convergence to Equilibrium Distribution, II. The Wave Equation in Odd Dimensions, with Mixing

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dc.creatorDudnikova, T. V.
dc.creatorKomech, A. I.
dc.creatorRatanov, N. E.
dc.creatorSuhov, Yu. M.
dc.date2005-08-19
dc.date.accessioned2026-07-07T04:32:17Z
dc.date.available2026-07-07T04:32:17Z
dc.descriptionThe paper considers the wave equation, with constant or variable coefficients in $\R^n$, with odd $n\geq 3$. We study the asymptotics of the distribution $μ_t$ of the random solution at time $t\in\R$ as $t\to\infty$. It is assumed that the initial measure $μ_0$ has zero mean, translation-invariant covariance matrices, and finite expected energy density. We also assume that $μ_0$ satisfies a Rosenblatt- or Ibragimov-Linnik-type space mixing condition. The main result is the convergence of $μ_t$ to a Gaussian measure $μ_\infty$ as $t\to\infty$, which gives a Central Limit Theorem (CLT) for the wave equation. The proof for the case of constant coefficients is based on an analysis of long-time asymptotics of the solution in the Fourier representation and Bernstein's `room-corridor' argument. The case of variable coefficients is treated by using a version of the scattering theory for infinite energy solutions, based on Vainberg's results on local energy decay.
dc.description27 pages
dc.identifierhttps://arxiv.org/abs/math-ph/0508039
dc.identifierhttp://arxiv.org/abs/math-ph/0508039
dc.identifierJournal of Statistical Physics 108 (2002), no.4, 1219-1253
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58132
dc.subjectMathematical Physics
dc.subjectProbability
dc.subject35L05, 60F05
dc.titleOn Convergence to Equilibrium Distribution, II. The Wave Equation in Odd Dimensions, with Mixing
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