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Spectral and probabilistic properties

of random walks on random graphs

New: Talks in PDF-Format



St. Kathrein

am Offenegg


The Alp-Workshop is meant to bring together people from probability theory and the spectral theory of operators. The goal of the workshop is a discussion concerning random graphs from the viewpoint of either of these two fields. Probabilistic aspects of the graph's randomness (e.g. independence, stationarity) and the nature of the random walk (e.g. recurrence) are opposed to spectral properties of the corresponding Laplacians (e.g. spectral radius, type of spectrum, density of states). In particular, spectral properties of percolation models and Erdös-Renyi random graphs will be among the fields of interest. The workshop will take place right after the 'Workshop on Boundaries', which is held in Graz between June 29th and July 4th.


Models of discrete probability theory such as percolation and random networks have, apart from their probabilistic content, a natural relationship to the spectral theory of linear operators. For example, the question of the nature of the spectrum of the Laplacian associated with a specific random walk on lamplighter groups has recently been shown to have a counterpart in percolation theory. On the other hand, the now classical problem of the random walk in random environment appears in the guise of the study of ergodic Jacobi matrices - mostly studied in mathematical physics. Old and new problems both of probability and spectral theory have common ground - at the alp-workshop, experts of both communities shall join in an ideal environment for an exchange of ideas.