The Parabolic Anderson Model
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The Parabolic Anderson Model
Author | : Wolfgang König |
Publsiher | : Birkhäuser |
Total Pages | : 192 |
Release | : 2016-06-30 |
Genre | : Mathematics |
ISBN | : 9783319335964 |
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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.
The Parabolic Anderson Model and Long range Percolation
Author | : Anonim |
Publsiher | : Unknown |
Total Pages | : 201 |
Release | : 2014 |
Genre | : Electronic Book |
ISBN | : OCLC:881611029 |
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Asymptotic Properties of the Parabolic Anderson Model
Author | : Anonim |
Publsiher | : Unknown |
Total Pages | : 81 |
Release | : 2011 |
Genre | : Electronic Book |
ISBN | : OCLC:918166094 |
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Parabolic Anderson Problem and Intermittency
Author | : René Carmona,Stanislav A. Molchanov |
Publsiher | : American Mathematical Soc. |
Total Pages | : 125 |
Release | : 1994 |
Genre | : Mathematics |
ISBN | : 9780821825778 |
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This book is devoted to the analysis of the large time asymptotics of the solutions of the heat equation in a random time-dependent potential. The authors give complete results in the discrete case of the $d$-dimensional lattice when the potential is, at each site, a Brownian motion in time. The phenomenon of intermittency of the solutions is discussed.
Precise Asymptotics for the Parabolic Anderson Model with a Moving Catalyst Or Trap
Author | : Adrian Schnitzler,Tilman Wolff |
Publsiher | : Unknown |
Total Pages | : 15 |
Release | : 2010 |
Genre | : Electronic Book |
ISBN | : OCLC:725561804 |
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Correlation Structure of Intermittency in the Parabolic Anderson Model
Author | : J. Gärtner,F. den Hollander |
Publsiher | : Unknown |
Total Pages | : 60 |
Release | : 1997 |
Genre | : Electronic Book |
ISBN | : OCLC:897840552 |
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Large Deviations
Author | : Frank Hollander |
Publsiher | : American Mathematical Soc. |
Total Pages | : 164 |
Release | : 2000 |
Genre | : Large deviations |
ISBN | : 0821844350 |
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Offers an introduction to large deviations. This book is divided into two parts: theory and applications. It presents basic large deviation theorems for i i d sequences, Markov sequences, and sequences with moderate dependence. It also includes an outline of general definitions and theorems.
Parabolic Anderson Model with Finite Number of Moving Catalysts
Author | : Fabienne Castell,Onur Gün,Gregory Maillard |
Publsiher | : Unknown |
Total Pages | : 24 |
Release | : 2011 |
Genre | : Electronic Book |
ISBN | : OCLC:781432939 |
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