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|a 9789811008498
|9 978-981-10-0849-8
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|a 10.1007/978-981-10-0849-8
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|a QA273.A1-274.9
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|a QA274-274.9
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|a MAT029000
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|a 519.2
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|a Funaki, Tadahisa.
|e author.
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|a Lectures on Random Interfaces
|h [electronic resource] /
|c by Tadahisa Funaki.
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|a Singapore :
|b Springer Singapore :
|b Imprint: Springer,
|c 2016.
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|a XII, 138 p. 44 illus., 9 illus. in color.
|b online resource.
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|a text
|b txt
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|a computer
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|a online resource
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|a text file
|b PDF
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|a SpringerBriefs in Probability and Mathematical Statistics,
|x 2365-4333
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|a 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 ∇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. 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(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 ill-posed SPDE and requires a renormalization. Especially its invariant measures are studied. .
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|a Mathematics.
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|a Partial differential equations.
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|a Probabilities.
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|a Mathematical physics.
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|a Mathematics.
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|a Probability Theory and Stochastic Processes.
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|a Partial Differential Equations.
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|a Mathematical Physics.
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|a SpringerLink (Online service)
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|t Springer eBooks
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|i Printed edition:
|z 9789811008481
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|a SpringerBriefs in Probability and Mathematical Statistics,
|x 2365-4333
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|u http://dx.doi.org/10.1007/978-981-10-0849-8
|z Full Text via HEAL-Link
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|a ZDB-2-SMA
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|a Mathematics and Statistics (Springer-11649)
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