Stochastic Loewner evolution driven by Levy processes
| dc.creator | Rushkin, I. | |
| dc.creator | Oikonomou, P. | |
| dc.creator | Kadanoff, L. P. | |
| dc.creator | Gruzberg, I. A. | |
| dc.date | 2005-09-07 | |
| dc.date | 2006-01-04 | |
| dc.date.accessioned | 2026-07-07T06:41:43Z | |
| dc.date.available | 2026-07-07T06:41:43Z | |
| dc.description | 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, $κ$, as well as $α$ 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 $\tilde{p}$, 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 $κ$ and $α$. It is reasonable to call such changes ``phase transitions''. These transitions occur as $κ$ passes through four (a well-known result) and as $α$ passes through one (a new result). Numerical simulations are then used to explore the associated touching and near-touching events. | |
| dc.description | Published version, minor typos corrected, added references | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0509187 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0509187 | |
| dc.identifier | J. Stat. Mech. (2006) P01001 | |
| dc.identifier | doi:10.1088/1742-5468/2006/01/P01001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/101771 | |
| dc.subject | Statistical Mechanics | |
| dc.title | Stochastic Loewner evolution driven by Levy processes | |
| dc.type | text |