Mathematics – Probability
Scientific paper
2002-01-15
Proceedings "Random walks and geometry", pp. 393-411, Vienna 2001, V. Kaimanovich ed., Walter de Gruyter, Berlin (2004)
Mathematics
Probability
Scientific paper
Random walks on general graphs play an important role in the understanding of the general theory of stochastic processes. Beyond their fundamental interest in probability theory, they arise also as simple models of physical systems. A brief survey of the physical relevance of the notion of random walk on both undirected and directed graphs is given followed by the exposition of some recent results on random walks on randomly oriented lattices. It is worth noticing that general undirected graphs are associated with (not necessarily Abelian) groups while directed graphs are associated with (not necessarily Abelian) $C^*$-algebras. Since quantum mechanics is naturally formulated in terms of $C^*$-algebras, the study of random walks on directed lattices has been motivated lately by the development of the new field of quantum information and communication.
Campanino Massimo
Petritis Dimitri
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