Brownian motion, random walks on trees, and harmonic measure on polynomial Julia sets
| dc.creator | Emerson, Nathaniel D. | |
| dc.date | 2006-09-04 | |
| dc.date | 2006-09-12 | |
| dc.date.accessioned | 2026-07-07T07:24:26Z | |
| dc.date.available | 2026-07-07T07:24:26Z | |
| dc.description | We consider the harmonic measure on a disconnected polynomial Julia set in terms of Brownian motion. We show that the harmonic measure of any connected component of such a Julia set is zero. Associated to the polynomial is a combinatorial model, the tree with dynamics. We define a measure on the tree, which is a combinatorial version on harmonic measure. We show that this measure is isomorphic to the harmonic measure on the Julia set. The measure induces a random walk on the tree, which is isomorphic to Brownian motion in the plane. | |
| dc.description | 15 pages, 5 figures. Revised 9/12/06 | |
| dc.identifier | https://arxiv.org/abs/math/0609044 | |
| dc.identifier | http://arxiv.org/abs/math/0609044 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/116348 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37F10 (Primary); 30C85, 05C8 (Secondary) | |
| dc.title | Brownian motion, random walks on trees, and harmonic measure on polynomial Julia sets | |
| dc.type | text |