SpringerBriefs in Probability and Mathematical Statistics

Lectures on Random Interfaces

Authors: Funaki, Tadahisa

  • Shows that the microscopic point of view is useful in choosing a real minimizer of a variational problem that determines an interface shape
  • Is the first book to discuss the stochastic extension of the Sharp interface limit for non-random PDEs
  • Is one of the few books dealing with the KPZ equation, a recent hot topic in probability theory
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書籍の購入

イーブック 41,64 €
価格の適用国: Japan (小計)
  • ISBN 978-981-10-0849-8
  • ウォーターマーク付、 DRMフリー
  • ファイル形式: PDF, EPUB
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ソフトカバー 49,99 €
価格の適用国: Japan (小計)
  • ISBN 978-981-10-0848-1
  • 個人のお客様には、世界中どこでも配送料無料でお届けします。
  • Usually dispatched within 3 to 5 business days.
この書籍について

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 ∇φ-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 dynamics is 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(φ)-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.    

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Table of contents (5 chapters)

  • Scaling Limits for Pinned Gaussian Random Interfaces in the Presence of Two Possible Candidates

    Funaki, Tadahisa

    Pages 1-28

    Preview Buy Chapter 26,95 €
  • Dynamic Young Diagrams

    Funaki, Tadahisa

    Pages 29-79

    Preview Buy Chapter 26,95 €
  • Stochastic Partial Differential Equations

    Funaki, Tadahisa

    Pages 81-92

    Preview Buy Chapter 26,95 €
  • Sharp Interface Limits for a Stochastic Allen-Cahn Equation

    Funaki, Tadahisa

    Pages 93-110

    Preview Buy Chapter 26,95 €
  • KPZ Equation

    Funaki, Tadahisa

    Pages 111-124

    Preview Buy Chapter 26,95 €

書籍の購入

イーブック 41,64 €
価格の適用国: Japan (小計)
  • ISBN 978-981-10-0849-8
  • ウォーターマーク付、 DRMフリー
  • ファイル形式: PDF, EPUB
  • どの電子書籍リーダーからでもすぐにお読みいただけます。
  • ご購入後、すぐにダウンロードしていただけます。
ソフトカバー 49,99 €
価格の適用国: Japan (小計)
  • ISBN 978-981-10-0848-1
  • 個人のお客様には、世界中どこでも配送料無料でお届けします。
  • Usually dispatched within 3 to 5 business days.
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書誌情報

Bibliographic Information
Book Title
Lectures on Random Interfaces
Authors
Series Title
SpringerBriefs in Probability and Mathematical Statistics
Copyright
2016
Publisher
Springer Singapore
Copyright Holder
The Author(s)
イーブック ISBN
978-981-10-0849-8
DOI
10.1007/978-981-10-0849-8
ソフトカバー ISBN
978-981-10-0848-1
Series ISSN
2365-4333
Edition Number
1
Number of Pages
XII, 138
Number of Illustrations and Tables
35 b/w illustrations, 9 illustrations in colour
Topics