Pathways in Mathematics: Random Walk in Random Potential

König, Wolfgang

This is a comprehensive survey on the research on the parabolic Anderson model – the heat equation with random potential or the random walk in random potential – of the years 1990 – 2015. The investigation of this model requires a combination of tools from probability (large deviations, extreme-value theory, e.g.) and analysis (spectral theory for the Laplace operator with potential, variational analysis, e.g.). We explain the background, the applications, the questions and the connections with other models and formulate the most relevant results on the long-time behavior of the solution, like quenched and annealed asymptotics for the total mass, intermittency, confinement and concentration properties and mass flow. Furthermore, we explain the most successful proof methods and give a list of open research problems. Proofs are not detailed, but concisely outlined and commented; the formulations of some theorems are slightly simplified for better comprehension.

Details

Published by: Birkhäuser

Publication Date: 2016-06-22

Format: Hardcover

ISBN-13: 9783319335957

DOI: 10.1007/978-3-319-33596-4

Dimensions: 235cm x155cm

Pages: 192