Percolation diffusion

Torbjörn Lundh

Stochastic Processes and their Applications, 2001, vol. 95, issue 2, 235-244

Abstract: Let a Brownian motion in the unit ball be absorbed if it hits a set generated by a radially symmetric Poisson point process. The point set is "fattened" by putting a ball with a constant hyperbolic radius on each point. When is the probability non-zero that the Brownian motion hits the boundary of the unit ball? That is, manage to avoid all the Poisson balls and "percolate diffusively" all the way to the boundary. We will show that if the bounded Poisson intensity at a point z is [nu](d(0,z)), where d(· ,·) is the hyperbolic metric, then the Brownian motion percolates diffusively if and only if n[nu][set membership, variant]L1.

Keywords: Percolation; Brownian; motion; Poisson; process; Hyperbolic; geometry; Minimal; thinness (search for similar items in EconPapers)
Date: 2001
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304-4149(01)00101-6
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:95:y:2001:i:2:p:235-244

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().