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Book synopsis

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.§

Book details

Book category Books in English Mathematics & science Mathematics Probability & statistics

• Full title: Parabolic Anderson Model
• Subtitle: Random Walk in Random Potential
• Author: Wolfgang König
• Language: English
• Binding: Hardback
• Number of pages: 192
• EAN: 9783319335957
• ISBN: 3319335952
• ID: 02975369
• Publisher: Birkhauser
• Weight: 4321 g
• Dimensions: 235 × 155 × 17 mm
• Date of publishing: 10. June 2016

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