|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'501'711
Articles rated: 2609
19 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Stochastic Loewner evolution driven by Levy processes | | I. Rushkin
; P. Oikonomou
; L. P. Kadanoff
; I. A. Gruzberg
; | | Date: |
7 Sep 2005 | | Subject: | Statistical Mechanics | cond-mat.stat-mech | | Affiliation: | The James Franck Institute, The University of Chicago | | Abstract: | Standard stochastic Loewner evolution (SLE) is driven by a continuous Brownian motion, which then produces a continuous fractal trace. If jumps are added to the driving function, the trace branches. We consider a generalized SLE driven by a superposition of a Brownian motion and a stable Levy process. The situation is defined by the usual SLE parameter, $kappa$, as well as $alpha$ which defines the shape of the stable Levy distribution. The resulting behavior is characterized by two descriptors: $p$, the probability that the trace self-intersects, and $ ilde{p}$, the probability that it will approach arbitrarily close to doing so. Using Dynkin’s formula, these descriptors are shown to change qualitatively and singularly at critical values of $kappa$ and $alpha$. It is reasonable to call such changes ``phase transitions’’. These transitions occur as $kappa$ passes through four (a well-known result) and as $alpha$ passes through one (a new result). Numerical simulations are then used to explore the associated touching and near-touching events. | | Source: | arXiv, cond-mat/0509187 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER