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＜電子ブック＞
The Parabolic Anderson Model : Random Walk in Random Potential / by Wolfgang König
(Pathways in Mathematics. ISSN:2367346X)

版	1st ed. 2016.
出版者	(Cham : Springer International Publishing : Imprint: Birkhäuser)
出版年	2016
大きさ	XI, 192 p. 4 illus : online resource
著者標目	*König, Wolfgang author SpringerLink (Online service)
件　名	LCSH:Probabilities LCSH:Mathematical physics FREE:Probability Theory FREE:Mathematical Physics FREE:Mathematical Methods in Physics
一般注記	1 Background, model and questions -- 2 Tools and concepts -- 3 Moment asymptotics for the total mass -- 4 Some proof techniques -- 5 Almost sure asymptotics for the total mass -- 6 Strong intermittency -- 7 Refined questions -- 8 Time-dependent potentials 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 HTTP:URL=https://doi.org/10.1007/978-3-319-33596-4

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