Fluctuations in Markov Processes

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Beschreibung

The present volume contains the most advanced theories on the martingale approach to central limit theorems. Using the time symmetry properties of the Markov processes, the book develops the techniques that allow us to deal with infinite dimensional models that appear in statistical mechanics and engineering (interacting particle systems, homogenization in random environments, and diffusion in turbulent flows, to mention just a few applications). The first part contains a detailed exposition of the method, and can be used as a text for graduate courses. The second concerns application to exclusion processes, in which the duality methods are fully exploited. The third part is about the homogenization of diffusions in random fields, including passive tracers in turbulent flows (including the superdiffusive behavior).

There are no other books in the mathematical literature that deal with this kind of approach to the problem of the central limit theorem. Hence, this volume meets the demand for a monograph on this powerful approach, now widely used in many areas of probability and mathematical physics. The book also covers the connections with and application to hydrodynamic limits and homogenization theory, so besides probability researchers it will also be of interest also to mathematical physicists and analysts.

Zusammenfassung

Unique in mathematical literature covers the most advanced theories about martingale approach to central limit theorems

Develops techniques that allow to deal with applications in statistical mechanics and engineering

Is of interest to probabilists, mathematical physicists and analysts

Includes supplementary material: [...]

Inhaltsverzeichnis

Preface.- Part I: General Theory.- 1.A Warming-up Example.- 2.Central Limit Theorems.- 3.RandomWalks in Random Environment.- 4.Bounds and Variational Principles for the Asymptotic Variance.- Part II: Simple Exclusion Processes.- 5.The Simple Exclusion Process.- 6.Self Diffusion.- 7.Equilibrium Fluctuations of the Density Field.- 8.Regularity of the Asymptotic Variance.- Part III: Diffusions in Random Environments.- 10.Variational Principles for the Limiting Variance.- 11.Diffusions with Divergence Free Drifts.- 12.Diffusions with Gaussian Drifts.- 13.Ornstein-Uhlenbeck Process with a Random Potential.- 14.Analytic Methods in Homogenization Theory.- References.- Notation.- Subject Index.

Erscheinungsjahr:	2014
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Grundlehren der mathematischen Wissenschaften
Inhalt:	xviii 494 S.
ISBN-13:	9783642428470
ISBN-10:	3642428479
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Komorowski, Tomasz Olla, Stefano Landim, Claudio
Hersteller:	Springer Berlin Springer Berlin Heidelberg Grundlehren der mathematischen Wissenschaften
Maße:	235 x 155 x 28 mm
Von/Mit:	Tomasz Komorowski (u. a.)
Erscheinungsdatum:	09.08.2014
Gewicht:	0,768 kg

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