2D growth processes: SLE and Loewner chains
By Michel Bauer, D. Bernard. 2006
181 citations recorded by the source corpus.
Abstract This review provides an introduction to two dimensional growth processes. Although it covers a variety of processes such as diffusion limited aggregation, it is mostly devoted to a detailed presentation of stochastic Schramm–Loewner evolutions (SLE) which are Markov processes describing interfaces in 2D critical systems. It starts with an informal discussion, using numerical simulations, of various examples of 2D growth processes and their connections with statistical mechanics. SLE is then introduced and Schramm's argument mapping conformally invariant interfaces to SLE is explained. A substantial part of the review is devoted to reveal the deep connections between statistical mechanics and processes, and more specifically to the present context, between 2D critical systems and SLE. Some of the remarkable properties of SLE are explained, together with the tools for computing with it. This review has been written with the aim of filling the gap between the mathematical and the physical literature on the subject.
Subfields: Condensed Matter Physics, Mathematical Physics, Molecular Biology
View Paper: https://www.semanticscholar.org/paper/65dc21442a1f91343819e5d11e2f62e4b215bac3
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In Condensed Matter Physics
- Julien Dubédat
- Scott Sheffield
- Stanislav Smirnov
- Wendelin Werner
- Gregory F. Lawler
- Oded Schramm
- Dmitry Chelkak
- Jason Miller
In Mathematical Physics
- Julien Dubédat
- Scott Sheffield
- Stanislav Smirnov
- Oded Schramm
- Wendelin Werner
- Gregory F. Lawler
- Dmitry Chelkak
- Jason Miller
In Molecular Biology
Citations in the corpus
- Towards conformal invariance of 2D lattice models (2007, background): “We do not discuss the general mathematical theory of SLE curves or their connections to physics, for which interested reader can consult the expository works [5], [10], [15], [41] and the book [22].”
- SLE and the free field: partition functions and couplings (2007, background): “For earlier considerations on partition functions/CFT correlators in relation with SLE, see [12, 2, 21] and references therein.”