Lectures on Random Interfaces
Language: English
Published by Springer Nature Singapore Jan 2017, 2017
Series: Book 3 of 12 - SpringerBriefs in Probability and Mathematical Statistics
- Softcover
- New
Seller: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, GermanyBuchWeltWeit Ludwig Meier e.K.
AbeBooks seller since January 11, 2012
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This item is printed on demand - it takes 3-4 days longer - Neuware -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 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(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. 152 pp. Englisch.…
Seller Inventory # 9789811008481
- Title
- Lectures on Random Interfaces
- Author
- Tadahisa Funaki
- Publisher
- Springer Nature Singapore Jan 2017
- 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
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BuchWeltWeit Ludwig Meier e.K.
Bergisch Gladbach, Germany
AbeBooks seller since January 11, 2012
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