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＜電子ブック＞
Lectures on Random Interfaces / by Tadahisa Funaki
(SpringerBriefs in Probability and Mathematical Statistics. ISSN:23654341)

版	1st ed. 2016.
出版者	Singapore : Springer Nature Singapore : Imprint: Springer
出版年	2016
本文言語	英語
大きさ	XII, 138 p. 44 illus., 9 illus. in color : online resource
著者標目	*Funaki, Tadahisa author SpringerLink (Online service)
件　名	LCSH:Probabilities LCSH:Differential equations LCSH:Mathematical physics FREE:Probability Theory FREE:Differential Equations FREE:Mathematical Physics
一般注記	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 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(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. HTTP:URL=https://doi.org/10.1007/978-981-10-0849-8

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