{"product_id":"9789811008481","title":"SpringerBriefs in Probability and Mathematical Statistics","description":"\u003ch1\u003eSpringerBriefs in Probability and Mathematical Statistics\u003c\/h1\u003e \u003ch2\u003eFunaki, Tadahisa\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cdiv\u003eInterfaces 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.\u003c\/div\u003e\u003cdiv\u003eAssuming 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.\u003c\/div\u003e\u003cdiv\u003eYoung 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.\u003c\/div\u003e\u003cdiv\u003eA 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.\u003c\/div\u003e\u003cdiv\u003eThe 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.    \u003c\/div\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2017-01-03\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9789811008481\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-981-10-0849-8\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 138\u003c\/p\u003e ","brand":"Springer Nature Singapore","offers":[{"title":"Default Title","offer_id":44522783015052,"sku":"9789811008481","price":49.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9789811008481.jpg?v=1775962887","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9789811008481","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}