LEADER 04078nam 22005655 450 001 9910157601403321 005 20220407184225.0 010 $a981-10-0849-3 024 7 $a10.1007/978-981-10-0849-8 035 $a(CKB)3710000001001561 035 $a(DE-He213)978-981-10-0849-8 035 $a(MiAaPQ)EBC4774016 035 $a(PPN)197453953 035 $a(EXLCZ)993710000001001561 100 $a20161227d2016 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aLectures on random interfaces /$fby Tadahisa Funaki 205 $a1st ed. 2016. 210 1$aSingapore :$cSpringer Singapore :$cImprint: Springer,$d2016. 215 $a1 online resource (XII, 138 p. 44 illus., 9 illus. in color.) 225 1 $aSpringerBriefs in Probability and Mathematical Statistics,$x2365-4333 311 $a981-10-0848-5 320 $aIncludes bibliographical references and index. 330 $aInterfaces are created to separate two distinct phases in a situation in which phase coexistence occurs. This book discusses randomly fluctuating interfaces in several different settings and from several points of view: discrete/continuum, microscopic/macroscopic, and static/dynamic theories. The following four topics in particular are dealt with in the book. Assuming that the interface is represented as a height function measured from a fixed-reference discretized hyperplane, the system is governed by the Hamiltonian of gradient of the height functions. This is a kind of effective interface model called ??-interface model. The scaling limits are studied for Gaussian (or non-Gaussian) random fields with a pinning effect under a situation in which the rate functional of the corresponding large deviation principle has non-unique minimizers. Young diagrams determine decreasing interfaces, and their dynamics are introduced. The large-scale behavior of such dynamics is studied from the points of view of the hydrodynamic limit and non-equilibrium fluctuation theory. Vershik curves are derived in that limit. A sharp interface limit for the Allen?Cahn equation, that is, a reaction?diffusion equation with bistable reaction term, leads to a mean curvature flow for the interfaces. Its stochastic perturbation, sometimes called a time-dependent Ginzburg?Landau model, stochastic quantization, or dynamic P(?)-model, is considered. Brief introductions to Brownian motions, martingales, and stochastic integrals are given in an infinite dimensional setting. The regularity property of solutions of stochastic PDEs (SPDEs) of a parabolic type with additive noises is also discussed. The Kardar?Parisi?Zhang (KPZ) equation , which describes a growing interface with fluctuation, recently has attracted much attention. This is an ill-posed SPDE and requires a renormalization. Especially its invariant measures are studied. . 410 0$aSpringerBriefs in Probability and Mathematical Statistics,$x2365-4333 606 $aProbabilities 606 $aDifferential equations, Partial 606 $aMathematical physics 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000 615 0$aProbabilities. 615 0$aDifferential equations, Partial. 615 0$aMathematical physics. 615 14$aProbability Theory and Stochastic Processes. 615 24$aPartial Differential Equations. 615 24$aMathematical Physics. 676 $a519.2 700 $aFunaki$b Tadahisa$4aut$4http://id.loc.gov/vocabulary/relators/aut$0499280 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910157601403321 996 $aLectures on random interfaces$91523422 997 $aUNINA