The Parabolic Anderson Model
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The Parabolic Anderson Model
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Author : Wolfgang König
language : en
Publisher: Birkhäuser
Release Date : 2016-06-30
The Parabolic Anderson Model written by Wolfgang König and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-30 with Mathematics categories.
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
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Author :
language : en
Publisher:
Release Date : 2014
The Parabolic Anderson Model And Long Range Percolation written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.
Asymptotic Properties Of The Parabolic Anderson Model
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Author :
language : en
Publisher:
Release Date : 2011
Asymptotic Properties Of The Parabolic Anderson Model written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.
Correlation Structure Of Intermittency In The Parabolic Anderson Model
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Author : J. Gärtner
language : en
Publisher:
Release Date : 1997
Correlation Structure Of Intermittency In The Parabolic Anderson Model written by J. Gärtner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with categories.
Long Time Tails In The Parabolic Anderson Model With Bounded Potential
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Author : Marek Biskup
language : en
Publisher:
Release Date : 2000
Long Time Tails In The Parabolic Anderson Model With Bounded Potential written by Marek Biskup and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with categories.
The Parabolic Anderson Model With Acceleration And Deceleration
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Author : Wolfgang König
language : en
Publisher:
Release Date : 2010
The Parabolic Anderson Model With Acceleration And Deceleration written by Wolfgang König and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with categories.
Parabolic Anderson Problem And Intermittency
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Author : René Carmona
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
Parabolic Anderson Problem And Intermittency written by René Carmona and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
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.
Probability In Complex Physical Systems
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Author : Jean-Dominique Deuschel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-04-23
Probability In Complex Physical Systems written by Jean-Dominique Deuschel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-23 with Mathematics categories.
Probabilistic approaches have played a prominent role in the study of complex physical systems for more than thirty years. This volume collects twenty articles on various topics in this field, including self-interacting random walks and polymer models in random and non-random environments, branching processes, Parisi formulas and metastability in spin glasses, and hydrodynamic limits for gradient Gibbs models. The majority of these articles contain original results at the forefront of contemporary research; some of them include review aspects and summarize the state-of-the-art on topical issues – one focal point is the parabolic Anderson model, which is considered with various novel aspects including moving catalysts, acceleration and deceleration and fron propagation, for both time-dependent and time-independent potentials. The authors are among the world’s leading experts. This Festschrift honours two eminent researchers, Erwin Bolthausen and Jürgen Gärtner, whose scientific work has profoundly influenced the field and all of the present contributions.
Large Deviations
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Author : Frank Hollander
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Large Deviations written by Frank Hollander and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This volume offers an introduction to large deviations. It is divided into two parts: theory and applications. Basic large deviation theorems are presented for i.i.d. sequences, Markov sequences, and sequences with moderate dependence. The rate function is computed explicitly. The theory is explained without too much emphasis on technicalities. Also included is an outline of general definitions and theorems. The goal is to expose the unified theme that gives large deviation theory its overall structure, which can be made to work in many concrete cases. The section on applications focuses on recent work in statistical physics and random media. This book contains 60 exercises (with solutions) that should elucidate the content and engage the reader. Prerequisites for the book are a strong background in probability and analysis and some knowledge of statistical physics. It would make an excellent textbook for a special topics course in large deviations.
The Parabolic Anderson Model On A Galton Watson Tree
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Author : Frank den Hollander
language : en
Publisher:
Release Date : 2020
The Parabolic Anderson Model On A Galton Watson Tree written by Frank den Hollander and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with categories.
We study the long-time asymptotics of the total mass of the solution to the parabolic Anderson model ( PAM) on a supercritical Galton-Watson random tree with bounded degrees. We identify the second-order contribution to this asymptotics in terms of a variational formula that gives information about the local structure of the region where the solution is concentrated. The analysis behind this formula suggests that, under mild conditions on the model parameters, concentration takes place on a tree with minimal degree. Our approach can be applied to finite locally tree-like random graphs, in a coupled limit where both time and graph size tend to infinity. As an example, we consider the configuration model or, more precisely, the uniform simple random graph with a prescribed degree sequence.