Séminaire du LPTMS: Y. Tourigny



LPTMS, salle 201, 2ème étage, Bât 100, Campus d'Orsay
15 Rue Georges Clemenceau, Orsay, 91405
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The Dyson-Schmidt approach to studying diffusion in a Levy environment

Yves Tourigny, Université de Bristol

A diffusion may be thought of as a certain limit of a corresponding random walk. When the environment is random, this limit is convenient because of the variety of analytical tools that can brought to bear on its study. This talk will be concerned with the approach pioneered by Bouchaud, Comtet, Georges and Le Doussal in 1990, which maps the diffusion problem to a disordered supersymmetric quantum problem. I shall review the Dyson-Schmidt method for the calculation of the Lyapunov exponent and of the density of states when the disorder is modelled by a Levy process. The interpretation of these self-averaging quantities in the context of difusion will be discussed, and a number of new « solvable » cases will be presented.

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