Lectures on Random Interfaces
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The work Lectures on Random Interfaces represents a distinct intellectual or artistic creation found in Boston University Libraries. This resource is a combination of several types including: Work, Language Material, Books.
The Resource
Lectures on Random Interfaces
Resource Information
The work Lectures on Random Interfaces represents a distinct intellectual or artistic creation found in Boston University Libraries. This resource is a combination of several types including: Work, Language Material, Books.
 Label
 Lectures on Random Interfaces
 Statement of responsibility
 by Tadahisa Funaki
 Subject

 Probability Theory and Stochastic Processes
 Mathematical physics
 Probabilities
 Partial differential equations
 Partial differential equations
 Mathematical physics
 Probabilities
 Mathematical Physics
 Electronic resources
 Mathematics
 Mathematical Physics
 Mathematics
 Partial Differential Equations
 Partial Differential Equations
 Language
 eng
 Summary
 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 fixedreference discretized hyperplane, the system is governed by the Hamiltonian of gradient of the height functions. This is a kind of effective interface model called ∇φinterface model. The scaling limits are studied for Gaussian (or nonGaussian) random fields with a pinning effect under a situation in which the rate functional of the corresponding large deviation principle has nonunique minimizers. Young diagrams determine decreasing interfaces, and their dynamics are introduced. The largescale behavior of such dynamics is studied from the points of view of the hydrodynamic limit and nonequilibrium 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 timedependent 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 illposed SPDE and requires a renormalization. Especially its invariant measures are studied.
 Image bit depth
 0
 LC call number

 QA273.A1274.9
 QA274274.9
 Literary form
 non fiction
 Series statement
 SpringerBriefs in Probability and Mathematical Statistics,
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