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The Parabolic Anderson Model: Random Walk in Random Potential (Pathways in Mathematics) - Tapa blanda

Libro 1 de 7: Pathways in Mathematics

König, Wolfgang

 
9783319815565: The Parabolic Anderson Model: Random Walk in Random Potential (Pathways in Mathematics)
Tapa blanda
ISBN 10: 3319815563 ISBN 13: 9783319815565
Editorial: Birkhäuser, 2018

Sinopsis

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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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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Editorial
Birkhäuser
Año de publicación
2018
Idioma
Inglés
ISBN 10 
3319815563
ISBN 13 
9783319815565
Encuadernación
Tapa blanda
Número de páginas
204
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