2D growth processes: SLE and Loewner chains

Details 2D growth processes: SLE and Loewner chains 2D growth processes: SLE and Loewner chains

2006-02-20

arxiv.org/abs/math-ph/0602049v1

Phys.Rept.432:115-221,2006

Physics

Mathematical Physics

A review on Stochastic Loewner evolutions for Physics Reports, 172 pages, low quality figures, better quality figures upon req

Scientific paper

10.1016/j.physrep.2006.06.002

This review provides an introduction to two dimensional growth processes. Although it covers a variety 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 SLE remarkable properties are explained, as well as the tools for computing with SLE. This review has been written with the aim of filling the gap between the mathematical and the physical literatures on the subject.

Affiliated with

Also associated with

No associations

Rating

2D growth processes: SLE and Loewner chains does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with 2D growth processes: SLE and Loewner chains, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and 2D growth processes: SLE and Loewner chains will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-520847