Mathematical Results In Quantum Mechanics - Proceedings Of The Qmath12 Conference (With Dvd-rom)
Mathematical Results In Quantum Mechanics - Proceedings Of The Qmath12 Conference (With Dvd-rom)

Author: Pavel Exner

Publisher: World Scientific

Published: 2014-11-13

Total Pages: 396

ISBN-13: 9814618152

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The book provides a comprehensive overview on the state of the art of the quantum part of mathematical physics. In particular, it contains contributions to the spectral theory of Schrödinger and random operators, quantum field theory, relativistic quantum mechanics and interacting many-body systems.It also presents an overview on the achievements in mathematical physics since the last conference QMath11 held at Hradec Kralove, Czechia in 2010.

The Parabolic Anderson Model
The Parabolic Anderson Model

Author: Wolfgang König

Publisher: Birkhäuser

Published: 2016-06-30

Total Pages: 199

ISBN-13: 3319335960

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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.

Mathematical Results In Quantum Physics - Proceedings Of The Qmath11 (With Dvd-rom)
Mathematical Results In Quantum Physics - Proceedings Of The Qmath11 (With Dvd-rom)

Author: Pavel Exner

Publisher: World Scientific

Published: 2011-05-26

Total Pages: 287

ISBN-13: 981446046X

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The volume collects papers from talks given at QMath11 — Mathematical Results in Quantum Physics, which was held in Hradec Králové, September 2010. These papers bring new and interesting results in quantum mechanics and information, quantum field theory, random systems, quantum chaos, as well as in the physics of social systems. Part of the contribution is dedicated to Ari Laptev on the occasion of his 60th birthday, in recognition of his mathematical results and his service to the community. The QMath conference series has played an important role in mathematical physics for more than two decades, typically attracting many of the best results achieved in the last three-year period, and the meeting in Hradec Králové was no exception.

Interacting Stochastic Systems
Interacting Stochastic Systems

Author: Jean-Dominique Deuschel

Publisher: Springer Science & Business Media

Published: 2005-01-12

Total Pages: 470

ISBN-13: 9783540230335

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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.

Probabilistic Methods in Telecommunications
Probabilistic Methods in Telecommunications

Author: Benedikt Jahnel

Publisher: Springer Nature

Published: 2020-06-17

Total Pages: 205

ISBN-13: 3030360903

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Probabilistic modeling and analysis of spatial telecommunication systems have never been more important than they are today. In particular, it is an essential research area for designing and developing next-generation communication networks that are based on multihop message transmission technology. These lecture notes provide valuable insights into the underlying mathematical discipline, stochastic geometry, introducing the theory, mathematical models and basic concepts. They also discuss the latest applications of the theory to telecommunication systems. The text covers several of the most fundamental aspects of quality of service: connectivity, coverage, interference, random environments, and propagation of malware. It especially highlights two important limiting scenarios of large spatial systems: the high-density limit and the ergodic limit. The book also features an analysis of extreme events and their probabilities based on the theory of large deviations. Lastly, it includes a large number of exercises offering ample opportunities for independent self-study.

In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius
In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius

Author: Maria Eulália Vares

Publisher: Springer Nature

Published: 2021-03-25

Total Pages: 819

ISBN-13: 3030607542

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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

Author: Jean-Dominique Deuschel

Publisher: Springer Science & Business Media

Published: 2012-04-23

Total Pages: 518

ISBN-13: 3642238114

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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.

Mathematics and Society
Mathematics and Society

Author: Wolfgang König

Publisher:

Published: 2016

Total Pages: 314

ISBN-13: 9783037196649

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The ubiquity and importance of mathematics in our complex society is generally not in doubt. However, even a scientifically interested layman would be hard pressed to point out aspects of our society where contemporary mathematical research is essential. Most popular examples are finance, engineering, wheather and industry, but the way mathematics comes into play is widely unknown in the public. And who thinks of application fields like biology, encryption, architecture, or voting systems? This volume comprises a number of success stories of mathematics in our society - important areas being shaped by cutting edge mathematical research. The authors are eminent mathematicians with a high sense for public presentation, addressing scientifically interested laymen as well as professionals in mathematics and its application disciplines.