2D growth processes: SLE and Loewner chains
Michel Bauer,Denis Bernard +1 more
TLDR
In this article, the authors present a detailed presentation of stochastic Schramm-Loewner evolutions (SLE) which are Markov processes describing interfaces in 2D critical systems.About:
This article is published in Physics Reports.The article was published on 2006-10-01 and is currently open access. It has received 215 citations till now. The article focuses on the topics: Schramm–Loewner evolution.read more
Citations
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Towards conformal invariance of 2D lattice models
TL;DR: In this article, the authors discuss how to prove the conformal invariance conjectures, especially in relation to Schramm�Loewner evolution, and show that these conjectures are false.
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Recent advances in percolation theory and its applications
TL;DR: In this paper, a variety of percolation models have been introduced some of which have completely different scaling and universal properties from the original model with either continuous or discontinuous transitions depending on the control parameter, dimensionality and the type of the underlying rules and networks.
Journal ArticleDOI
Recent advances in percolation theory and its applications
TL;DR: The basic features of the ordinary model are outlined and a glimpse at a number of selective variations and modifications of the original model are taken and a connection with the magnetic models is established.
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SLE and the free field: partition functions and couplings
TL;DR: In this article, the authors studied the relationship between the Schramm-Loewner evolution and the free field in planar simply connected domains and established identities of partition functions between different versions of the evolution with appropriate boundary conditions, including the Polyakov-Alvarez conformal anomaly formula.
Book
Non-Equilibrium Statistical Mechanics and Turbulence
TL;DR: In this paper, three harmonised lecture courses by world class experts in statistical physics and turbulence are presented, including Field Theory and Non-Equilibrium Statistical Mechanics; Gregory Falkovich discusses Turbulence Theory as part of Statistical Physics; and Krzysztof Gawedzki examines Soluble Models of Turbulent Transport.
References
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The Fractal Geometry of Nature
TL;DR: This book is a blend of erudition, popularization, and exposition, and the illustrations include many superb examples of computer graphics that are works of art in their own right.
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Phase Transitions and Critical Phenomena
TL;DR: The field of phase transitions and critical phenomena continues to be active in research, producing a steady stream of interesting and fruitful results as discussed by the authors, and the major aim of this serial is to provide review articles that can serve as standard references for research workers in the field.
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Stochastic differential equations : an introduction with applications
TL;DR: Some Mathematical Preliminaries as mentioned in this paper include the Ito Integrals, Ito Formula and the Martingale Representation Theorem, and Stochastic Differential Equations.
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Infinite Conformal Symmetry in Two-Dimensional Quantum Field Theory
TL;DR: In this paper, the authors present an investigation of the massless, two-dimentional, interacting field theories and their invariance under an infinite-dimensional group of conformal transformations.
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Diffusion-limited aggregation, a kinetic critical phenomenon
Abstract: A model for random aggregates is studied by computer simulation The model is applicable to a metal-particle aggregation process whose correlations have been measured previously Density correlations within the model aggregates fall off with distance with a fractional power law, like those of the metal aggregates The radius of gyration of the model aggregates has power-law behavior The model is a limit of a model of dendritic growth