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# ðŸ“™ The Parabolic Anderson Model: Random Walk in Random Potential by Wolfgang KÃ¶nig (auth.) â€” free epub

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This is a comprehensive survey on the research on the parabolic Anderson model â€“ the heat equation with random potential or the random walk in random potential â€“ of the years 1990 â€“ 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.

- Series:
**Pathways in Mathematics** - Author:
**Wolfgang KÃ¶nig (auth.)** - Year:
**2016** - Publisher:
**BirkhÃ¤user Basel** - Language:
**English** - ISBN:
**978-3-319-33595-7, 978-3-319-33596-4**

- File size:
**2 596 275** - Format:
**pdf**

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The simplest mathematical model of the Brownian motion of physics is the simple, symmetric random walk. This book collects and compares current results - mostly strong theorems which describe the properties of a random walk. The modern problems of the lim...

Random walks have proven to be a useful model in understanding processes across a wide spectrum of scientific disciplines. Elements of the Random Walk is an introduction to some of the most powerful and general techniques used in the application of these ...

Classical probability theory provides information about random walks after a fixed number of steps. For applications, however, it is more natural to consider random walks evaluated after a random number of steps. Stopped Random Walks: Limit Theorems and A...

Classical probability theory provides information about random walks after a fixed number of steps. For applications, however, it is more natural to consider random walks evaluated after a random number of steps. Stopped Random Walks: Limit Theorems and A...

Emanating from the theory of C*-algebras and actions of tori theoren, the problems discussed here are outgrowths of random walk problems on lattices. An AGL (d,Z)-invariant (which is a partially ordered commutative algebra) is obtained for lattice polytop...

This book is devoted exclusively to a very special class of random processes, namely to random walk on the lattice points of ordinary Euclidean space. The author considered this high degree of specialization worthwhile, because of the theory of such rando...

Combining three books into a single volume, this text comprises Multicolor Problems, dealing with several of the classical map-coloring problems; Problems in the Theory of Numbers, an elementary introduction to algebraic number theory; and Random Walks, a...

This book is a lucid, straightforward introduction to the concepts and techniques of statistical physics that students of biology, biochemistry, and biophysics must know. It provides a sound basis for understanding random motions of molecules, subcellular...

Moderate Deviations for the Range of Planar Random Walks...

Sudbury, Ontario is one of the world's most polluted areas. A century of industrial activities has resulted in thousands of acidified lakes and vast areas of denuded land. This book describes, in a manner accessible to a wide audience, the damage and the ...

In the two decades since the development of the first eclipsing-binary modeling code, new analytic techniques and the availability of powerful, sometimes dedicated computing facilities have made possible vastly improved determinations of fundamental and e...

This book reviews the shifting conceptions of writing and revision, noting the ways in which views of knowledge and knowing shape teaching and research. Fitzgerald, as a reading and writing researcher, recognizes that how we revise is shaped by how we rea...

It is estimated that the functionally significant body of knowledge for a given medical specialty changes radically every 8 years. New specialÂ ties and "sub-specialization" are occurring at approximately an equal rate. Historically, established journals ...

Three additional sections have been added in this edition in response to stuÂ dents' suggestions. A short summary of motor deficits, a brief discussion of craÂ nial nerve functions and some examples of localizing signs of anatomic lesions should prove hel...

The emotional impact of having a newborn hospitalized in an intensive care unit is immense. The parents' perceptions of the child's fragility and of their role in the vulnerable child's life represent important facts of the crisis in which the infant and ...

This book is concerned with the psychological effects of unemployment. In writing it I had two main aims: (1) to describe theoretical approaches that are relevant to understanding unemployment effects; and (2) to present the reÂ sults of studies from a pr...

The KES-IDT-2016 proceedings give an excellent insight into recent research, both theoretical and applied, in the field of intelligent decision making. The range of topics explored is wide, and covers methods of grouping, classification, prediction, decis...