The Parabolic Anderson Model

Random Walk in Random Potential

By:

Wolfgang Konig

Format:

Paperback / softback

Series:

Pathways in Mathematics

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Description

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.

Release date Australia

May 31st, 2018

Author

Wolfgang Konig

Audience

Professional & Vocational

Edition

Softcover reprint of the original 1st ed. 2016

Illustrations

4 Illustrations, black and white; XI, 192 p. 4 illus.

Pages

192

Series

Pathways in Mathematics

Dimensions

156x234x11

ISBN-13

9783319815565

Product ID

28206713

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