Poisson point processes, excursions and stable processes in two-dimensional structures
type: Item
instance of: scholarly article
title: Poisson point processes, excursions and stable processes in two-dimensional structures
zbMATH Open document ID: 1203.60052
author: Wendelin Werner
published in: Stochastic Processes and their Applications
publication date: 2010-05-21T00:00:00Z
review text: This is a non-formal survey of some processes and measures, connected with two-dimensional stochastic structures. In this relation there are considered a Brownian motion on the plane, a Poisson process of two-dimensional excursions inside a disk, a point field of self-intersections and a Poisson field of loops of the Brownian motion. A connection these structures with the Ising model on the plane is noted. A common property of these structures is invariance of their distributions with respect to conformal transformations of the plane.
Mathematics Subject Classification ID: 60G55
Mathematics Subject Classification ID: 60G18
Mathematics Subject Classification ID: 60J55
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60J67
zbMATH DE Number: 5710803
zbMATH Keywords: excursions
zbMATH Keywords: Poisson point process
zbMATH Keywords: Brownian motion
zbMATH Keywords: Bessel processes
zbMATH Keywords: Schramm-Loewner evolutions
zbMATH Keywords: conformal transformations
zbMATH Keywords: loop soups
zbMATH Keywords: Ising model
reviewed by: B. P. Harlamov
MaRDI profile type: Publication
full work available at URL: j.spa.2010.01.014
OpenAlex ID: W2061870695
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DOI: 10.1016/J.SPA.2010.01.014
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description: scientific article; zbMATH DE number 5710803