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Lectures on Random Interfaces: (SpringerBriefs in Probability and Mathematical Statistics)

Lectures on Random Interfaces: (SpringerBriefs in Probability and Mathematical Statistics)

          
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About the Book

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 ?f-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 dynamicsis 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(f)-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.    

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Product Details
  • ISBN-13: 9789811008481
  • Publisher: Springer Verlag, Singapore
  • Publisher Imprint: Springer Verlag, Singapore
  • Edition: 1st ed. 2016
  • Language: English
  • Returnable: Y
  • Spine Width: 0 mm
  • Width: 155 mm
  • ISBN-10: 9811008485
  • Publisher Date: 03 Jan 2017
  • Binding: Paperback
  • Height: 235 mm
  • No of Pages: 138
  • Series Title: SpringerBriefs in Probability and Mathematical Statistics
  • Weight: 2687 gr


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