{"product_id":"9789811008481","title":"Lectures on Random Interfaces","description":"\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 dynamics is 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\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003ePublication Year: \u003c\/strong\u003e2016\u003cbr\u003e\u003cstrong\u003eImprint: \u003c\/strong\u003eSpringer Singapore\u003cbr\u003e\u003cstrong\u003e\u003c\/strong\u003eFormat: P\u003cbr\u003e\u003cstrong\u003e\u003c\/strong\u003eWeight (Gram): 2685\u003cbr\u003e\u003cstrong\u003e\u003c\/strong\u003e\u003cbr\u003e\u003cstrong\u003e\u003c\/strong\u003e\u003cbr\u003e\u003cstrong\u003e\u003c\/strong\u003e\u003cbr\u003e\u003cstrong\u003e\u003c\/strong\u003e\u003cbr\u003e\u003cstrong\u003e\u003c\/strong\u003e\u003cbr\u003e\u003cstrong\u003e\u003c\/strong\u003e\u003c\/p\u003e","brand":"Tadahisa Funaki","offers":[{"title":"Default Title","offer_id":41265564221618,"sku":"9789811008481","price":77.99,"currency_code":"SGD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0502\/5382\/4178\/products\/9811008485.01_SCLZZZZZZZ.jpg?v=1636021061","url":"https:\/\/readabook.store\/products\/9789811008481","provider":"READABOOK BY ALKEM","version":"1.0","type":"link"}