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Teoreticheskaya i Matematicheskaya Fizika, 1991, Volume 87, Number 2, Pages 254–273 (Mi tmf5490)  

This article is cited in 1 scientific paper (total in 1 paper)

Mean-field models in the theory of random media. III

L. V. Bogachev, S. A. Molchanov
References:
Abstract: In the mean-field (nonlocal) diffusion approximation, when the Laplacian $\Delta$ on the lattice $\mathbf Z^d$ is replaced by the corresponding operator $\overline\Delta_V$ in a volume $V\subset\mathbf Z^d$ $(|V|\to\infty)$ [1, 2], a study is made of the $t\to\infty$ asymptotics of the statistical moments (moment functions) $m_p=m_p(\mathbf x_1,\dots,\mathbf x_p, t)=\langle\psi(\mathbf x_1,t,\omega)\dots\psi(\mathbf x_p,t,\omega)\rangle$, $p=1,2,\dots,$ for the evolution equation $\partial\psi/\partial t=\varkappa\Delta_V\psi+\xi\psi$ with nonstationary random potential $\xi=\xi(\mathbf x,t,\omega)$. The case when $\xi$ represents Gaussian white noise (with respect to $t$) is considered in the paper. At the same time, the evolution equation in such a medium is understood in the sense of It$\operatorname{\hat o}$. In space, the potential $\xi$ is assumed either to be localized, $\xi(\mathbf x,t,\omega)=\delta(\mathbf x_0,\mathbf x)\xi(\mathbf x_0,t,\omega)$, or homogeneous, namely, $\delta$-correlated with respect to $\mathbf x$. Under these conditions, the exponent $\gamma_p=\displaystyle\lim_{t\to\infty}t^{-1}\ln m_p$ is calculated.
Received: 05.10.1990
English version:
Theoretical and Mathematical Physics, 1991, Volume 87, Issue 2, Pages 512–526
DOI: https://doi.org/10.1007/BF01016124
Bibliographic databases:
Language: Russian
Citation: L. V. Bogachev, S. A. Molchanov, “Mean-field models in the theory of random media. III”, TMF, 87:2 (1991), 254–273; Theoret. and Math. Phys., 87:2 (1991), 512–526
Citation in format AMSBIB
\Bibitem{BogMol91}
\by L.~V.~Bogachev, S.~A.~Molchanov
\paper Mean-field models in the theory of random media.~III
\jour TMF
\yr 1991
\vol 87
\issue 2
\pages 254--273
\mathnet{http://mi.mathnet.ru/tmf5490}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1129666}
\zmath{https://zbmath.org/?q=an:0729.60059}
\transl
\jour Theoret. and Math. Phys.
\yr 1991
\vol 87
\issue 2
\pages 512--526
\crossref{https://doi.org/10.1007/BF01016124}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1991GR75800008}
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  • https://www.mathnet.ru/eng/tmf/v87/i2/p254
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