The Parabolic Anderson Model

The Parabolic Anderson Model PDF Author: Wolfgang König
Publisher: Birkhäuser
ISBN: 3319335960
Category : Mathematics
Languages : en
Pages : 199

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Book Description
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

The Parabolic Anderson Model PDF Author: Wolfgang König
Publisher: Birkhäuser
ISBN: 3319335960
Category : Mathematics
Languages : en
Pages : 199

Get Book Here

Book Description
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.

Interacting Stochastic Systems

Interacting Stochastic Systems PDF Author: Jean-Dominique Deuschel
Publisher: Springer Science & Business Media
ISBN: 9783540230335
Category : Computers
Languages : en
Pages : 470

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Book Description
The Research Network on "Interacting stochastic systems of high complexity" set up by the German Research Foundation aimed at exploring and developing connections between research in infinite-dimensional stochastic analysis, statistical physics, spatial population models from mathematical biology, complex models of financial markets or of stochastic models interacting with other sciences. This book presents a structured collection of papers on the core topics, written at the close of the 6-year programme by the research groups who took part in it. The structure chosen highlights the interweaving of certain themes and certain interconnections discovered through the joint work. This yields a reference work on results and methods that will be useful to all who work between applied probability and the physical, economic, and life sciences.

Large Deviations

Large Deviations PDF Author: Frank Hollander
Publisher: American Mathematical Soc.
ISBN: 9780821844359
Category : Mathematics
Languages : en
Pages : 164

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Book Description
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.

In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius

In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius PDF Author: Maria Eulália Vares
Publisher: Springer Nature
ISBN: 3030607542
Category : Mathematics
Languages : en
Pages : 819

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Book Description
This is a volume in memory of Vladas Sidoravicius who passed away in 2019. Vladas has edited two volumes appeared in this series ("In and Out of Equilibrium") and is now honored by friends and colleagues with research papers reflecting Vladas' interests and contributions to probability theory.

Probability in Complex Physical Systems

Probability in Complex Physical Systems PDF Author: Jean-Dominique Deuschel
Publisher: Springer Science & Business Media
ISBN: 3642238114
Category : Mathematics
Languages : en
Pages : 518

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Book Description
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.

Mighty Stories, Dangerous Rituals

Mighty Stories, Dangerous Rituals PDF Author: Herbert Anderson
Publisher: Fortress Press
ISBN: 1506454801
Category : Religion
Languages : en
Pages : 236

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Book Description
Shaping our journey into the Divine This moving and enlightening book presents us with a compelling vision of what can happen when we take the opportunity to connect stories and rituals--a vision of individuals and communities transformed through a deeper sense of connection to our loved ones, our communities, and God. Herbert Anderson and Edward Foley reveal how when stories and rituals work together, they have the potential to be both mighty and dangerous--mighty in their ability to lift us up and help us make these connections beyond ourselves and dangerous in challenging us to learn to live with complexity and contradiction. They show how much more meaningful a baptism, wedding, or funeral can be when liturgy is made to include and recognize the personal stories of those involved. Suddenly, these familiar life-cycle rituals are infused with new life as participants become connected in a narrative web linking past and present, human and divine. Newly created rituals can also help us connect our stories to the divine story, giving meaning to what we experience and bringing us closer to God. Ministers, worship leaders, and pastoral caregivers can use this approach to storytelling and ritual to find ways to bring together worship and pastoral care.

Analysis of Stochastic Partial Differential Equations

Analysis of Stochastic Partial Differential Equations PDF Author: Davar Khoshnevisan
Publisher: American Mathematical Soc.
ISBN: 147041547X
Category : Mathematics
Languages : en
Pages : 127

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Book Description
The general area of stochastic PDEs is interesting to mathematicians because it contains an enormous number of challenging open problems. There is also a great deal of interest in this topic because it has deep applications in disciplines that range from applied mathematics, statistical mechanics, and theoretical physics, to theoretical neuroscience, theory of complex chemical reactions [including polymer science], fluid dynamics, and mathematical finance. The stochastic PDEs that are studied in this book are similar to the familiar PDE for heat in a thin rod, but with the additional restriction that the external forcing density is a two-parameter stochastic process, or what is more commonly the case, the forcing is a "random noise," also known as a "generalized random field." At several points in the lectures, there are examples that highlight the phenomenon that stochastic PDEs are not a subset of PDEs. In fact, the introduction of noise in some partial differential equations can bring about not a small perturbation, but truly fundamental changes to the system that the underlying PDE is attempting to describe. The topics covered include a brief introduction to the stochastic heat equation, structure theory for the linear stochastic heat equation, and an in-depth look at intermittency properties of the solution to semilinear stochastic heat equations. Specific topics include stochastic integrals à la Norbert Wiener, an infinite-dimensional Itô-type stochastic integral, an example of a parabolic Anderson model, and intermittency fronts. There are many possible approaches to stochastic PDEs. The selection of topics and techniques presented here are informed by the guiding example of the stochastic heat equation. A co-publication of the AMS and CBMS.

Hypersonic and High Temperature Gas Dynamics

Hypersonic and High Temperature Gas Dynamics PDF Author: John David Anderson
Publisher: AIAA
ISBN: 9781563474590
Category : Science
Languages : en
Pages : 710

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Book Description
This book is a self-contained text for those students and readers interested in learning hypersonic flow and high-temperature gas dynamics. It assumes no prior familiarity with either subject on the part of the reader. If you have never studied hypersonic and/or high-temperature gas dynamics before, and if you have never worked extensively in the area, then this book is for you. On the other hand, if you have worked and/or are working in these areas, and you want a cohesive presentation of the fundamentals, a development of important theory and techniques, a discussion of the salient results with emphasis on the physical aspects, and a presentation of modern thinking in these areas, then this book is also for you. In other words, this book is designed for two roles: 1) as an effective classroom text that can be used with ease by the instructor, and understood with ease by the student; and 2) as a viable, professional working tool for engineers, scientists, and managers who have any contact in their jobs with hypersonic and/or high-temperature flow.

Fourier Analysis and Nonlinear Partial Differential Equations

Fourier Analysis and Nonlinear Partial Differential Equations PDF Author: Hajer Bahouri
Publisher: Springer Science & Business Media
ISBN: 3642168302
Category : Mathematics
Languages : en
Pages : 530

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Book Description
In recent years, the Fourier analysis methods have expereinced a growing interest in the study of partial differential equations. In particular, those techniques based on the Littlewood-Paley decomposition have proved to be very efficient for the study of evolution equations. The present book aims at presenting self-contained, state- of- the- art models of those techniques with applications to different classes of partial differential equations: transport, heat, wave and Schrödinger equations. It also offers more sophisticated models originating from fluid mechanics (in particular the incompressible and compressible Navier-Stokes equations) or general relativity. It is either directed to anyone with a good undergraduate level of knowledge in analysis or useful for experts who are eager to know the benefit that one might gain from Fourier analysis when dealing with nonlinear partial differential equations.

Stochastic Models

Stochastic Models PDF Author: Donald Andrew Dawson
Publisher: American Mathematical Soc.
ISBN: 9780821810637
Category : Mathematics
Languages : en
Pages : 492

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Book Description
This book presents the refereed proceedings of the International Conference on Stochastic Models held in Ottawa (ON, Canada) in honor of Professor Donald A. Dawson. Contributions to the volume were written by students and colleagues of Professor Dawson, many of whom are eminent researchers in their own right. A main theme of the book is the development and study of the Dawson-Watanabe "superprocess", a fundamental building block in modelling interaction particle systems undergoing reproduction and movement. The volume also contains an excellent review article by Professor Dawson and a complete list of his work. This comprehensive work offers a wide assortment of articles on Markov processes, branching processes, mathematical finance, filtering, queueing networks, time series, and statistics. It should be of interest to a broad mathematical audience.