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Lectures on Random Interfaces
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 fo...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore :
Springer Nature Singapore : Imprint: Springer,
2016.
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| Edición: | 1st ed. 2016. |
| Colección: | SpringerBriefs in Probability and Mathematical Statistics,
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| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
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| 245 | 1 | 0 | |a Lectures on Random Interfaces |h [electronic resource] / |c by Tadahisa Funaki. |
| 250 | |a 1st ed. 2016. | ||
| 264 | 1 | |a Singapore : |b Springer Nature Singapore : |b Imprint: Springer, |c 2016. | |
| 300 | |a XII, 138 p. 44 illus., 9 illus. in color. |b online resource. | ||
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| 520 | |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. . | ||
| 650 | 0 | |a Probabilities. | |
| 650 | 0 | |a Differential equations. | |
| 650 | 0 | |a Mathematical physics. | |
| 650 | 1 | 4 | |a Probability Theory. |
| 650 | 2 | 4 | |a Differential Equations. |
| 650 | 2 | 4 | |a Mathematical Physics. |
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| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||