Fluctuation of planar Brownian loop capturing large area
| dc.creator | Hammond, Alan | |
| dc.creator | Peres, Yuval | |
| dc.date | 2004-11-24 | |
| dc.date | 2005-06-07 | |
| dc.date.accessioned | 2026-07-07T05:14:39Z | |
| dc.date.available | 2026-07-07T05:14:39Z | |
| dc.description | We consider a planar Brownian loop $B$ that is run for a time $T$ and conditioned on the event that its range encloses the unusually high area of $πT^2$, with $T$ being large. We study the deviation of the range of the conditioned process $X$ from a circle of radius $T$, as a model for the fluctuation of a phase boundary. This deviation is measured by means of the inradius and outradius of the region enclosed by the range of $X$. We prove that in a typical realization of the conditioned measure, each of these quantities differs from $T$ by at most $T^{2/3 + ε}$. | |
| dc.description | 39 pages with six figures: minor revisions to earlier version | |
| dc.identifier | https://arxiv.org/abs/math/0411540 | |
| dc.identifier | http://arxiv.org/abs/math/0411540 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73357 | |
| dc.subject | Probability | |
| dc.subject | Mathematical Physics | |
| dc.title | Fluctuation of planar Brownian loop capturing large area | |
| dc.type | text |