Results On The Parabolic Anderson Model
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| Author | : Wolfgang König |
| Publisher | : Birkhäuser |
| Total Pages | : 199 |
| Release | : 2016-06-30 |
| Genre | : Mathematics |
| ISBN | : 3319335960 |
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.
| Author | : Jean-Dominique Deuschel |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 518 |
| Release | : 2012-04-23 |
| Genre | : Mathematics |
| ISBN | : 3642238114 |
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.
| Author | : Jean-Dominique Deuschel |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 470 |
| Release | : 2005-01-12 |
| Genre | : Computers |
| ISBN | : 9783540230335 |
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.
| Author | : Donald Andrew Dawson |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 492 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : 9780821810637 |
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.
| Author | : Tadahisa Funaki |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 319 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461384680 |
This IMA Volume in Mathematics and its Applications NONLINEAR STOCHASTIC PDEs: HYDRODYNAMIC LIMIT AND BURGERS' TURBULENCE is based on the proceedings of the period of concentration on Stochas tic Methods for Nonlinear PDEs which was an integral part of the 1993- 94 IMA program on "Emerging Applications of Probability." We thank Tadahisa Funaki and Wojbor A. Woyczynski for organizing this meeting and for editing the proceedings. We also take this opportunity to thank the National Science Foundation and the Army Research Office, whose financial support made this workshop possible. A vner Friedman Willard Miller, Jr. xiii PREFACE A workshop on Nonlinear Stochastic Partial Differential Equations was held during the week of March 21 at the Institute for Mathematics and Its Applications at the University of Minnesota. It was part of the Special Year on Emerging Applications of Probability program put together by an organizing committee chaired by J. Michael Steele. The selection of topics reflected personal interests of the organizers with two areas of emphasis: the hydrodynamic limit problems and Burgers' turbulence and related models. The talks and the papers appearing in this volume reflect a number of research directions that are currently pursued in these areas.
| Author | : René Carmona |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 138 |
| Release | : 1994 |
| Genre | : Mathematics |
| ISBN | : 0821825771 |
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.
| Author | : Jean-Dominique Deuschel |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 443 |
| Release | : 2005-12-05 |
| Genre | : Mathematics |
| ISBN | : 3540271104 |
Core papers emanating from the research network, DFG-Schwerpunkt: Interacting stochastic systems of high complexity.
| Author | : Wilfried Grecksch |
| Publisher | : World Scientific |
| Total Pages | : 261 |
| Release | : 2020-04-22 |
| Genre | : Science |
| ISBN | : 9811209804 |
This volume contains survey articles on various aspects of stochastic partial differential equations (SPDEs) and their applications in stochastic control theory and in physics.The topics presented in this volume are:This book is intended not only for graduate students in mathematics or physics, but also for mathematicians, mathematical physicists, theoretical physicists, and science researchers interested in the physical applications of the theory of stochastic processes.
| Author | : Jochen Blath |
| Publisher | : European Mathematical Society |
| Total Pages | : 270 |
| Release | : 2011 |
| Genre | : Mathematics |
| ISBN | : 9783037190722 |
The 33rd Bernoulli Society Conference on Stochastic Processes and Their Applications was held in Berlin from July 27 to July 31, 2009. It brought together more than 600 researchers from 49 countries to discuss recent progress in the mathematical research related to stochastic processes, with applications ranging from biology to statistical mechanics, finance and climatology. This book collects survey articles highlighting new trends and focal points in the area written by plenary speakers of the conference, all of them outstanding international experts. A particular aim of this collection is to inspire young scientists to pursue research goals in the wide range of fields represented in this volume.
| Author | : Elena Celledoni |
| Publisher | : Springer |
| Total Pages | : 734 |
| Release | : 2019-01-13 |
| Genre | : Mathematics |
| ISBN | : 3030015939 |
The Abel Symposia volume at hand contains a collection of high-quality articles written by the world’s leading experts, and addressing all mathematicians interested in advances in deterministic and stochastic dynamical systems, numerical analysis, and control theory. In recent years we have witnessed a remarkable convergence between individual mathematical disciplines that approach deterministic and stochastic dynamical systems from mathematical analysis, computational mathematics and control theoretical perspectives. Breakthrough developments in these fields now provide a common mathematical framework for attacking many different problems related to differential geometry, analysis and algorithms for stochastic and deterministic dynamics. In the Abel Symposium 2016, which took place from August 16-19 in Rosendal near Bergen, leading researchers in the fields of deterministic and stochastic differential equations, control theory, numerical analysis, algebra and random processes presented and discussed the current state of the art in these diverse fields. The current Abel Symposia volume may serve as a point of departure for exploring these related but diverse fields of research, as well as an indicator of important current and future developments in modern mathematics.
