Lectures on Random Interfaces

Language: English

Published by Springer, 2017

9811008485 / 9789811008481

Series: Book 3 of 12 - SpringerBriefs in Probability and Mathematical Statistics

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Seller: AHA-BUCH GmbH, Einbeck, GermanyAHA-BUCH GmbH

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Druck auf Anfrage Neuware - Printed after ordering - Interfaces are created to separate two distinct phases in a situation in which phase coexistence occurs. This book discusses randomly fluctuating interfaces in several different settings and from several points of view: discrete/continuum, microscopic/macroscopic, and static/dynamic theories. The following four topics in particular are dealt with in the book.Assuming that the interface is represented as a height function measured from a fixed-reference discretized hyperplane, the system is governed by the Hamiltonian of gradient of the height functions. This is a kind of effective interface model called phi-interface model. The scaling limits are studied for Gaussian (or non-Gaussian) random fields with a pinning effect under a situation in which the rate functional of the corresponding large deviation principle has non-unique minimizers.Young diagrams determine decreasing interfaces, and their dynamics are introduced. The large-scale behavior of such dynamicsis studied from the points of view of the hydrodynamic limit and non-equilibrium fluctuation theory. Vershik curves are derived in that limit.A sharp interface limit for the Allen-Cahn equation, that is, a reaction-diffusion equation with bistable reaction term, leads to a mean curvature flow for the interfaces. Its stochastic perturbation, sometimes called a time-dependent Ginzburg-Landau model, stochastic quantization, or dynamic P(phi)-model, is considered. Brief introductions to Brownian motions, martingales, and stochastic integrals are given in an infinite dimensional setting. The regularity property of solutions of stochastic PDEs (SPDEs) of a parabolic type with additive noises is also discussed.The Kardar-Parisi-Zhang (KPZ) equation , which describes a growing interface with fluctuation, recently has attracted much attention. This is an ill-posed SPDE and requires a renormalization. Especially its invariant measures are studied.…

Seller Inventory # 9789811008481

Title
Lectures on Random Interfaces
Author
Tadahisa Funaki
Publisher
Springer
Publication year
2017
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
9811008485
ISBN 13
9789811008481
Item weight
270 grams
Dimensions
235x155x9 mm
Series
Book 3 of 12: SpringerBriefs in Probability and Mathematical Statistics

AHA-BUCH GmbH

Einbeck, Germany

5-star seller

AbeBooks seller since August 14, 2006

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