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Maximal entropy random walk : solvable cases of dynamics

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Maximal entropy random walk : solvable cases of dynamics

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dc.contributor.author Ochab, Jeremi [SAP14013682] pl
dc.date.accessioned 2016-06-08T16:26:56Z
dc.date.available 2016-06-08T16:26:56Z
dc.date.issued 2012 pl
dc.identifier.issn 0587-4254 pl
dc.identifier.uri http://ruj.uj.edu.pl/xmlui/handle/item/27685
dc.language eng pl
dc.rights Udzielam licencji. Uznanie autorstwa - Użycie niekomercyjne 3.0 Polska *
dc.rights.uri http://creativecommons.org/licenses/by-nc/3.0/pl/legalcode *
dc.title Maximal entropy random walk : solvable cases of dynamics pl
dc.type JournalArticle pl
dc.description.physical 1143-1155 pl
dc.abstract.en We focus on the study of dynamics of two kinds of random walk: generic random walk (GRW) and maximal entropy random walk (MERW) on two model networks: Cayley trees and ladder graphs. The stationary probability distribution for MERW is given by the squared components of the eigenvector associated with the largest eigenvalue λ0 of the adjacency matrix of a graph, while the dynamics of the probability distribution approaching to the stationary state depends on the second largest eigenvalue λ1. Firstly, we give analytic solutions for Cayley trees with arbitrary branching number, root degree, and number of generations. We determine three regimes of a tree structure corresponding to strongly, critically, and weakly branched roots. Each of them results in different statics and dynamics of MERW. We show how the relaxation times, generically shorter for MERW than for GRW, scale with the graph size. Secondly, we give numerical results for ladder graphs with symmetric defects. MERW shows a clear exponential growth of the relaxation time with the size of defective regions, which indicates trapping of a particle within highly entropic intact region and its escaping that resembles quantum tunneling through a potential barrier. GRW shows standard diffusive dependence irrespective of the defects. pl
dc.description.volume 43 pl
dc.description.number 5 pl
dc.identifier.doi 10.5506/APhysPolB.43.1143 pl
dc.identifier.eissn 1509-5770 pl
dc.title.journal Acta Physica Polonica. B pl
dc.title.volume XXIV Marian Smoluchowski Symposium on Statistical Physics, Insights into Stochastic Nonequilibrium pl
dc.language.container eng pl
dc.affiliation Wydział Fizyki, Astronomii i Informatyki Stosowanej : Instytut Fizyki im. Mariana Smoluchowskiego pl
dc.subtype Article pl
dc.rights.original CC-BY; otwarte czasopismo; ostateczna wersja wydawcy; w momencie opublikowania; 0 pl
.pointsMNiSW [2012 A]: 20


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Udzielam licencji. Uznanie autorstwa - Użycie niekomercyjne 3.0 Polska Except where otherwise noted, this item's license is described as Udzielam licencji. Uznanie autorstwa - Użycie niekomercyjne 3.0 Polska