https://doi.org/10.1140/epjst/e2010-01232-1
Review
Markov chains or the game of structure and chance
From complex networks, to language evolution, to musical compositions
1 Department of Physics, University of Bielefeld, Postfach 100131, 33501 Bielefeld, Germany
2 Center of Excellence Cognitive Interaction Technology (CITEC), University of Bielefeld, Postfach 10 01 31, 33501 Bielefeld, Germany
a e-mail: blanchard@physik.uni-bielefeld.de
b e-mail: jean_rene.dawin@uni-bielefeld.de
c e-mail: volchenk@physik.uni-bielefeld.de
Markov chains provide us with a powerful tool for studying the structure of graphs and databases in details. We review the method of generalized inverses for Markov chains and apply it for the analysis of urban structures, evolution of languages, and musical compositions. We also discuss a generalization of Lévy flights over large complex networks and study the interplay between the nonlinearity of diffusion process and the topological structure of the network.
© EDP Sciences, Springer-Verlag, 2010
