The Parabolic Anderson Model

Download or Read eBook The Parabolic Anderson Model PDF written by Wolfgang König and published by Birkhäuser. This book was released on 2016-06-30 with total page 199 pages. Available in PDF, EPUB and Kindle.
The Parabolic Anderson Model
Author :
Publisher : Birkhäuser
Total Pages : 199
Release :
ISBN-10 : 9783319335964
ISBN-13 : 3319335960
Rating : 4/5 (64 Downloads)

Book Synopsis The Parabolic Anderson Model by : Wolfgang König

Book excerpt: 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.


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