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Steady‐state random walk on connected graph of arbitrary topology with random and non‐symmetric transition rates
Author(s) -
Taraskin S. N.
Publication year - 2013
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.201248526
Subject(s) - random walk , topology (electrical circuits) , mathematics , random graph , transition (genetics) , statistical physics , random walker algorithm , boundary (topology) , random variable , simple (philosophy) , graph , transition rate matrix , combinatorics , discrete mathematics , physics , mathematical analysis , statistics , biochemistry , chemistry , philosophy , epistemology , gene
The general solution and its graphical interpretation for the stationary occupation probability of nodes for a random‐walk on a connected network of arbitrary topology with random and non‐symmetric transition rates are presented. Configurational averaging over the quenched random transition rates is performed for several simple networks: open chains, simple and general stars, two interacting stars. It is demonstrated that disorder in transition rates for a random walker induces variable occupation probability for different nodes in the network depending on their location. The boundary nodes are shown to be occupied with higher probability than the central ones.