Brownian Motion, Obstacles and Random Media

Author: Alain-Sol Sznitman

Publisher: Springer Science & Business Media

ISBN: 3662112817

Category: Mathematics

Page: 357

View: 6298

This book provides an account for the non-specialist of the circle of ideas, results and techniques, which grew out in the study of Brownian motion and random obstacles. It also includes an overview of known results and connections with other areas of random media, taking a highly original and personal approach throughout.

Dynamics and Randomness II

Author: Alejandro Maass,Servet Martínez,Jaime San Martín

Publisher: Springer Science & Business Media

ISBN: 9781402019906

Category: Mathematics

Page: 228

View: 9151

This book contains the lectures given at the Second Conference on Dynamics and Randomness held at the Centro de Modelamiento Matemático of the Universidad de Chile, from December 9-13, 2003. This meeting brought together mathematicians, theoretical physicists, theoretical computer scientists, and graduate students interested in fields related to probability theory, ergodic theory, symbolic and topological dynamics. The courses were on: -Some Aspects of Random Fragmentations in Continuous Times; -Metastability of Ageing in Stochastic Dynamics; -Algebraic Systems of Generating Functions and Return Probabilities for Random Walks; -Recurrent Measures and Measure Rigidity; -Stochastic Particle Approximations for Two-Dimensional Navier Stokes Equations; and -Random and Universal Metric Spaces. The intended audience for this book is Ph.D. students on Probability and Ergodic Theory as well as researchers in these areas. The particular interest of this book is the broad areas of problems that it covers. We have chosen six main topics and asked six experts to give an introductory course on the subject touching the latest advances on each problem.

Directed Polymers in Random Environments

École d'Été de Probabilités de Saint-Flour XLVI – 2016

Author: Francis Comets

Publisher: Springer

ISBN: 3319504878

Category: Mathematics

Page: 199

View: 1605

Analyzing the phase transition from diffusive to localized behavior in a model of directed polymers in a random environment, this volume places particular emphasis on the localization phenomenon. The main questionis: What does the path of a random walk look like if rewards and penalties are spatially randomly distributed?This model, which provides a simplified version of stretched elastic chains pinned by random impurities, has attracted much research activity, but it (and its relatives) still holds many secrets, especially in high dimensions. It has non-gaussian scaling limits and it belongs to the so-called KPZ universality class when the space is one-dimensional. Adopting a Gibbsian approach, using general and powerful tools from probability theory, the discrete model is studied in full generality. Presenting the state-of-the art from different perspectives, and written in the form of a first course on the subject, this monograph is aimed at researchers in probability or statistical physics, but is also accessible to masters and Ph.D. students.

Random Operators

Author: Michael Aizenman,Simone Warzel

Publisher: American Mathematical Soc.

ISBN: 1470419130

Category: Functional analysis -- Miscellaneous applications of functional analysis -- Applications in quantum physics

Page: 326

View: 7608

This book provides an introduction to the mathematical theory of disorder effects on quantum spectra and dynamics. Topics covered range from the basic theory of spectra and dynamics of self-adjoint operators through Anderson localization--presented here via the fractional moment method, up to recent results on resonant delocalization. The subject's multifaceted presentation is organized into seventeen chapters, each focused on either a specific mathematical topic or on a demonstration of the theory's relevance to physics, e.g., its implications for the quantum Hall effect. The mathematical chapters include general relations of quantum spectra and dynamics, ergodicity and its implications, methods for establishing spectral and dynamical localization regimes, applications and properties of the Green function, its relation to the eigenfunction correlator, fractional moments of Herglotz-Pick functions, the phase diagram for tree graph operators, resonant delocalization, the spectral statistics conjecture, and related results. The text incorporates notes from courses that were presented at the authors' respective institutions and attended by graduate students and postdoctoral researchers.

Stochastic Analysis on Large Scale Interacting Systems

Author: Tadahisa Funaki,Hirofumi Osada

Publisher: Mathematical Soc of Japan


Category: Mathematics

Page: 395

View: 6960

This volume is a collection of 15 research and survey papers written by the speakers from two international conferences held in Japan, The 11th Mathematical Society of Japan International Research Institute's Stochastic Analysis on Large Scale Interacting Systems and Stochastic Analysis and Statistical Mechanics. Topics discussed in the volume cover the hydrodynamic limit, fluctuations, large deviations, spectral gap (Poincare inequality), logarithmic Sobolev inequality, Ornstein-Zernike asymptotics, random environments, determinantal expressions for systems including exclusion processes (stochastic lattice gas, Kawasaki dynamics), zero range processes, interacting Brownian particles, random walks, self-avoiding walks, Ginzburg-Landau model, interface models, Ising model, Widom-Rowlinson model, directed polymers, random matrices, Dyson's model, and more. The material is suitable for graduate students and researchers interested in probability theory, stochastic processes, and statistical mechanics.

Annales de l'I.H.P.

Probabilités et statistiques

Author: N.A

Publisher: N.A


Category: Probabilities

Page: N.A

View: 1175

Dirichlet Forms and Analysis on Wiener Space

Author: Nicolas Bouleau,Francis Hirsch

Publisher: Walter de Gruyter

ISBN: 311085838X

Category: Mathematics

Page: 335

View: 2785

The subject of this book is analysis on Wiener space by means of Dirichlet forms and Malliavin calculus. There are already several literature on this topic, but this book has some different viewpoints. First the authors review the theory of Dirichlet forms, but they observe only functional analytic, potential theoretical and algebraic properties. They do not mention the relation with Markov processes or stochastic calculus as discussed in usual books (e.g. Fukushima’s book). Even on analytic properties, instead of mentioning the Beuring-Deny formula, they discuss “carré du champ” operators introduced by Meyer and Bakry very carefully. Although they discuss when this “carré du champ” operator exists in general situation, the conditions they gave are rather hard to verify, and so they verify them in the case of Ornstein-Uhlenbeck operator in Wiener space later. (It should be noticed that one can easily show the existence of “carré du champ” operator in this case by using Shigekawa’s H-derivative.) In the part on Malliavin calculus, the authors mainly discuss the absolute continuity of the probability law of Wiener functionals. The Dirichlet form corresponds to the first derivative only, and so it is not easy to consider higher order derivatives in this framework. This is the reason why they discuss only the first step of Malliavin calculus. On the other hand, they succeeded to deal with some delicate problems (the absolute continuity of the probability law of the solution to stochastic differential equations with Lipschitz continuous coefficients, the domain of stochastic integrals (Itô-Ramer-Skorokhod integrals), etc.). This book focuses on the abstract structure of Dirichlet forms and Malliavin calculus rather than their applications. However, the authors give a lot of exercises and references and they may help the reader to study other topics which are not discussed in this book. Zentralblatt Math, Reviewer: S.Kusuoka (Hongo)

Stochastic Integrals

An Introduction

Author: Heinrich von Weizsäcker

Publisher: Springer-Verlag

ISBN: 3663139239

Category: Mathematics

Page: 332

View: 1994

Random Polymers

Author: Frank Hollander

Publisher: Springer Science & Business Media

ISBN: 364200332X

Category: Mathematics

Page: 258

View: 6676

Polymer chains that interact with themselves and/or their environment display a range of physical and chemical phenomena. This text focuses on the mathematical description of some of these phenomena, offering a mathematical panorama of polymer chains.


Einführung in die Wahrscheinlichkeitstheorie und Statistik

Author: Hans-Otto Georgii

Publisher: Walter de Gruyter

ISBN: 3110206773

Category: Mathematics

Page: 389

View: 3504

Der Text bietet eine Einführung in die Wahrscheinlichkeitstheorie und Statistik, wobei die beiden genannten Fachgebiete in zwei separaten Teilen gleichberechtigt nebeneinander gestellt sind. Im Unterschied zu vielen anderen einführenden Lehrbüchern erfolgt keine Trennung in diskrete und allgemeine Modelle. Die dritte Auflage enthält zahlreiche neue Illustrationen und aktualisierte Übungsaufgaben. Einführung in die zentralen Ideen der Wahrscheinlichkeitstheorie. Überaus positive Aufnahme der ersten beiden Auflagen. Zahlreiche für die 3. Auflage aktualisierte Anwendungs- und Übungsbeispiele.

Mathematik für Physiker und Ingenieure 1

Basiswissen für das Grundstudium - mit mehr als 1400 Aufgaben und Lösungen online

Author: Klaus Weltner

Publisher: Springer-Verlag

ISBN: 3642300855

Category: Science

Page: 301

View: 3734

Das zweibändige Lehrwerk bietet eine gut verständliche Einführung in die mathematischen Grundlagen des Physik- und Ingenieurstudiums. Band 1 richtet sich an Studierende im ersten Semester (Bachelor). Die Lerninhalte werden begleitet von Erläuterungen zu den einzelnen Übungsschritten (Rückfragen, Aufgaben und Lösungen), welche auch online zur Verfügung stehen. Daher eignet sich das seit über 25 Jahren bewährte Lehrbuch hervorragend für das Selbststudium. Die 17. Auflage wurde überarbeitet und ergänzt.

Vito Volterra

Author: Angelo Guerraggio,Giovanni Paoloni

Publisher: Springer-Verlag

ISBN: 3034800819

Category: Mathematics

Page: 230

View: 6017

Der Mathematiker Vito Volterra (1860 – 1940) war nicht nur ein großer Mathematiker, sondern auch ein guter Wissenschaftsorganisator. Über Jahrzehnte galt er als der bedeutendste Repräsentant der Wissenschaft in Italien. Die Autoren rekonstruieren seine wichtigsten Beiträge zur Wissenschaft und zur Entwicklung der wissenschaftlichen Institutionen in Italien und der Welt: von der Entwicklung der Funktionalanalysis über die Untersuchung der Populationsdynamik bis zu seiner Lehrtätigkeit und der Gründung des staatlichen italienischen Forschungsrates.

Lokal präsentierbare Kategorien

Author: Peter Gabriel,Friedrich Ulmer

Publisher: Springer-Verlag

ISBN: 3540368868

Category: Mathematics

Page: 200

View: 9082

Bernhard Riemann 1826–1866

Wendepunkte in der Auffassung der Mathematik

Author: Detlef Laugwitz

Publisher: Springer-Verlag

ISBN: 3034889836

Category: Mathematics

Page: 348

View: 9764

Das Riemannsche Integral lernen schon die Schüler kennen, die Theorien der reellen und der komplexen Funktionen bauen auf wichtigen Begriffsbildungen und Sätzen Riemanns auf, die Riemannsche Geometrie ist für Einsteins Gravitationstheorie und ihre Erweiterungen unentbehrlich, und in der Zahlentheorie ist die berühmte Riemannsche Vermutung noch immer offen. Riemann und sein um fünf Jahre jüngerer Freund Richard Dedekind sahen sich als Schüler von Gauss und Dirichlet. Um die Mitte des 19. Jahrhunderts leiteten sie den Übergang zur "modernen Mathematik" ein, der eine in Analysis und Geometrie, der andere in der Algebra mit der Hinwendung zu Mengen und Strukturen. Dieses Buch ist der erste Versuch, Riemanns wissenschaftliches Werk unter einem einheitlichen Gesichtspunkt zusammenzufassend darzustellen. Riemann gilt als einer der Philosophen unter den Mathematikern. Er stellte das Denken in Begriffen neben die zuvor vorherrschende algorithmische Auffassung von der Mathematik, welche die Gegenstände der Untersuchung, in Formeln und Figuren, in Termumformungen und regelhaften Konstruktionen als die allein legitimen Methoden sah. David Hilbert hat als Riemanns Grundsatz herausgestellt, die Beweise nicht durch Rechnung, sondern lediglich durch Gedanken zu zwingen. Hermann Weyl sah als das Prinzip Riemanns in Mathematik und Physik, "die Welt als das erkenntnistheoretische Motiv..., die Welt aus ihrem Verhalten im un- endlich kleinen zu verstehen."