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Lectures on Random Interfaces

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Lectures on Random Interfaces/ by Tadahisa Funaki.
作者:	Funaki, Tadahisa.
面頁冊數:	XII, 138 p. 44 illus., 9 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Probabilities. -
電子資源:	https://doi.org/10.1007/978-981-10-0849-8
ISBN:	9789811008498

Lectures on Random Interfaces
Funaki, Tadahisa.

Lectures on Random Interfaces[electronic resource] /by Tadahisa Funaki. - 1st ed. 2016. - XII, 138 p. 44 illus., 9 illus. in color.online resource. - SpringerBriefs in Probability and Mathematical Statistics,2365-4333. - SpringerBriefs in Probability and Mathematical Statistics,.

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. .

ISBN: 9789811008498

Standard No.: 10.1007/978-981-10-0849-8doiSubjects--Topical Terms:

527847
Probabilities.

LC Class. No.: QA273.A1-274.9

Dewey Class. No.: 519.2

Lectures on Random Interfaces
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