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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.201341621
Subject(s) - random walk , topology (electrical circuits) , random graph , statistical physics , mathematics , graph , boundary (topology) , transition (genetics) , network topology , transition rate matrix , random variable , diffusion , computer science , physics , discrete mathematics , combinatorics , mathematical analysis , statistics , biochemistry , chemistry , gene , thermodynamics , operating system
Heterogeneity is a factor inherent for many transport phenomena. It is a challenging theoretical task to deal with disorder and, in particular, to average the observables over different realisation of disorder. In the paper by S. N. Taraskin ( pp. 1029–1043 ), a theoretical model for diffusion on a network of arbitrary topology with non‐symmetric random transition rates is developed and solved analytically for the steady‐state regime. 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.