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The Resource Lectures on Random Interfaces

Lectures on Random Interfaces

Label
Lectures on Random Interfaces
Title
Lectures on Random Interfaces
Creator
Subject
Language
eng
Member of
Cataloging source
MiAaPQ
Literary form
non fiction
Nature of contents
dictionaries
Series statement
SpringerBriefs in Probability and Mathematical Statistics Ser.
Series volume
v.Vol. 2
Lectures on Random Interfaces
Label
Lectures on Random Interfaces
Link
http://libproxy.rpi.edu/login?url=https://ebookcentral.proquest.com/lib/rpi/detail.action?docID=4774016
Publication
Copyright
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Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • Preface -- Contents -- 1 Scaling Limits for Pinned Gaussian Random Interfaces in the Presence of Two Possible Candidates -- 1.1 Macroscopic Variational Problems -- 1.1.1 Wulff Shape and Winterbottom Shape -- 1.1.2 Variational Problem with Two Media -- 1.1.3 Variational Problem with a Pinning Effect -- 1.1.4 Examples of Minimizers of J with a Pinning Effect -- 1.2 Microscopic Models -- 1.2.1 Wulff Shape from Microscopic Models -- 1.2.2 The z-Interface Model with a Pinning -- 1.3 Results for d=1, n{u2265}1 -- 1.4 Outline of the Proof -- 1.5 Results for d{u2265}3, n=1 -- 1.6 Outline of the Proof -- 1.6.1 Proof of the Lower Bound -- 1.6.2 Proof of the Upper Bound -- 1.6.3 Proof of the Large Deviation Type Estimate -- 2 Dynamic Young Diagrams -- 2.1 Static Theory of 2D Young Diagrams -- 2.1.1 Ensembles of 2D Young Diagrams -- 2.1.2 Scaling Limits, Law of Large Numbers, and Vershik Curves -- 2.1.3 Central Limit Theorem -- 2.1.4 Large Deviation Principle -- 2.1.5 Equivalence of Ensembles under Inhomogeneous Conditioning -- 2.1.6 Related Young Diagrams -- 2.2 Dynamic Theory of 2D Young Diagrams -- 2.2.1 Dynamics of 2D Young Diagrams and Their Gradient Fields -- 2.2.2 Hydrodynamic Limits (LLN) -- 2.2.3 Non-Equilibrium Fluctuations -- 2.2.4 Dynamic Large Deviation Principle -- 2.2.5 Conservative Systems -- 2.3 3D Young Diagrams -- 2.3.1 Static Theory -- 2.3.2 Dynamic Theory -- 3 Stochastic Partial Differential Equations -- 3.1 The TDGL Equation -- 3.2 White Noise, Colored Noise, and Stochastic Integrals -- 3.3 SPDEs of Parabolic Type with Additive Noises -- 3.3.1 Two Definitions of Solutions -- 3.3.2 Regularity of Solutions -- 3.3.3 Invariant Measures -- 4 Sharp Interface Limits for a Stochastic Allen-Cahn Equation -- 4.1 Setting, Quick Overview and Background -- 4.2 Sharp Interface Limits in a Stochastic Case
  • 4.2.1 One-Dimensional Case with Space-Time White Noise -- 4.2.2 Higher-Dimensional Case with Noise Asymptotically White in Time -- 4.3 A Brief Survey and Supplements -- 4.3.1 Deterministic Case -- 4.3.2 Stochastic Case -- 5 KPZ Equation -- 5.1 The KPZ Equation, Its Ill-Posedness, and Its Renormalization -- 5.2 Cole-Hopf Solution and the Linear Stochastic Heat Equation -- 5.3 KPZ Approximating Equations -- 5.3.1 Simple Approximation -- 5.3.2 Approximation Adapted to Studying Invariant Measures -- 5.4 Passing to the Limit "3223379 0 -- 5.5 Invariant Measures of the Cole-Hopf Solution and SHE -- 5.6 Multi-component Coupled KPZ Equation -- References -- Index
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Dimensions
unknown
http://library.link/vocab/discovery_link
{'f': 'http://opac.lib.rpi.edu/record=b4387181'}
Extent
1 online resource (147 pages)
Form of item
online
Isbn
9789811008498
Media category
computer
Media MARC source
rdamedia
Media type code
c
Sound
unknown sound
Specific material designation
remote

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