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Teoreticheskaya i Matematicheskaya Fizika, 1993, Volume 94, Number 3, Pages 496–514 (Mi tmf1439)  

This article is cited in 10 scientific papers (total in 10 papers)

Random walks in disordered systems with long-range transitions. Asymptotically exactly solvable models

F. S. Dzheparov, V. E. Shestopal

Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
References:
Abstract: Random-jump models of transport in disordered system are studied. They are described by the master equation $\dot P=-{\mathcal A}\xi P$, where $-{\mathcal A}$ is the generator of the spatially and temporary uniform random walks process on a regular lattice, $\xi$ is the diagonal operator, $\xi _{xy}=\xi _x \delta _{xy}$, where $\{\xi _x\}$ are independent positive random variables with the same distribution. The case is elaborated when ${\mathcal A}_{xy}={\mathcal A}_{yx}={\mathcal A}_{x-y,0}$, the transition rates are determined by multipole-type interactions and $\{\xi _x\}$ have several first negative moments (the random-jump-rate model – with unbounded jumps). Methods of asymptotical expansion of the propagator for small Laplace parameter values and for long times are developed. It is made also by means of functional integral representation. The influence of disorder and of interaction power on the long-time asymptotics is considered. A method of investigation for system with a forced drift along a certain direction is suggested. Some methods of reciprocal transformation of asymptotically–exactly solvable problems are discussed and linkages with other known models are demonstrated. The $l_1$-norm of resolvent is obtained for any Markov process with a countable set of states and $l_1$-bounded generator.
Received: 07.05.1992
English version:
Theoretical and Mathematical Physics, 1993, Volume 94, Issue 3, Pages 345–357
DOI: https://doi.org/10.1007/BF01017267
Bibliographic databases:
Language: Russian
Citation: F. S. Dzheparov, V. E. Shestopal, “Random walks in disordered systems with long-range transitions. Asymptotically exactly solvable models”, TMF, 94:3 (1993), 496–514; Theoret. and Math. Phys., 94:3 (1993), 345–357
Citation in format AMSBIB
\Bibitem{DzhShe93}
\by F.~S.~Dzheparov, V.~E.~Shestopal
\paper Random walks in disordered systems with long-range transitions. Asymptotically exactly solvable models
\jour TMF
\yr 1993
\vol 94
\issue 3
\pages 496--514
\mathnet{http://mi.mathnet.ru/tmf1439}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1226226}
\transl
\jour Theoret. and Math. Phys.
\yr 1993
\vol 94
\issue 3
\pages 345--357
\crossref{https://doi.org/10.1007/BF01017267}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1993MA71000013}
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  • https://www.mathnet.ru/eng/tmf1439
  • https://www.mathnet.ru/eng/tmf/v94/i3/p496
  • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:76
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