Lectures on random interfaces / / by Tadahisa Funaki

• Autore: Funaki Tadahisa
• Pubblicazione: Singapore : , : Springer Singapore : , : Imprint : Springer, , 2016
• Edizione: 1st ed. 2016.
• Descrizione fisica: 1 online resource (XII, 138 p. 44 illus., 9 illus. in color.)
• Disciplina: 519.2
• Soggetto topico: Probabilities; Differential equations, Partial; Mathematical physics; Probability Theory and Stochastic Processes; Partial Differential Equations; Mathematical Physics
• Nota di bibliografia: Includes bibliographical references and index.
• 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–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. .
• Titolo autorizzato: Lectures on random interfaces
• ISBN: 981-10-0849-3
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910157601403321
• Lo trovi qui: Univ. Federico II
• Serie: SpringerBriefs in Probability and Mathematical Statistics, . 2365-4333