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[null,"1.","Record Nr.",null,"UNINA9910157601403321"]
[null,null,"Autore",null,"Funaki Tadahisa"]
[null,null,"Titolo",null,"Lectures on random interfaces / / by Tadahisa Funaki"]
[null,null,"Pubbl/distr/stampa",null,"Singapore : , : Springer Singapore : , : Imprint : Springer, , 2016"]
[null,null,"ISBN",null,"981-10-0849-3"]
[null,null,"Edizione",null,"[1st ed. 2016.]"]
[null,null,"Descrizione fisica",null,"1 online resource (XII, 138 p. 44 illus., 9 illus. in color.)"]
[null,null,"Collana",null,"SpringerBriefs in Probability and Mathematical Statistics, , 2365-4333"]
[null,null,"Disciplina",null,"519.2"]
[null,null,"Soggetti",null,"Probabilities"]
[{"$nulls":4},"Differential equations, Partial"]
[{"$nulls":4},"Mathematical physics"]
[{"$nulls":4},"Probability Theory and Stochastic Processes"]
[{"$nulls":4},"Partial Differential Equations"]
[{"$nulls":4},"Mathematical Physics"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Nota di bibliografia","Includes bibliographical references and index."]
[null,null,null,"Sommario/riassunto","Interfaces are created to separate two distinct phases in a situation in which phase coexistence occurs. This book discusses randomly fluctuating interfaces in several different settings and from several points of view: discrete/continuum, microscopic/macroscopic, and static/dynamic theories. The following four topics in particular are dealt with in the book. Assuming that the interface is represented as a height function measured from a fixed-reference discretized hyperplane, the system is governed by the Hamiltonian of gradient of the height functions. This is a kind of effective interface model called ∇φ-interface model. The scaling limits are studied for Gaussian (or non-Gaussian) random fields with a pinning effect under a situation in which the rate functional of the corresponding large deviation principle has non-unique minimizers. Young diagrams determine decreasing interfaces, and their dynamics are introduced. The large-scale behavior of such dynamics is studied from the points of view of the hydrodynamic limit and non-equilibrium fluctuation theory. Vershik curves are derived in that limit. A sharp interface limit for the Allen–Cahn equation, that is, a reaction–diffusion equation with bistable reaction term, leads to a mean curvature flow for the interfaces. Its stochastic perturbation, sometimes called a time-dependent Ginzburg–"]
[{"$nulls":4},"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. ."]