Intersection exponents for planar Brownian motion
type: Item
instance of: scholarly article
title: Intersection exponents for planar Brownian motion
zbMATH Open document ID: 0965.60071
author: Gregory F. Lawler
author: Wendelin Werner
published in: The Annals of Probability
publication date: 2001-07-25T00:00:00Z
review text: This paper establishes new properties of the intersection exponents for planar Brownian motion. The intersection exponent \(\xi(n,p)\) is defined by \(P(t) \approx t^{-\xi(n,p)/2}\) where \(P(t)\) is the probability that two packets of \(n\) resp. \(p\) independent Brownian motions do not intersect each other before time \(t\). The main results are the following: the definition of \(\xi\) is naturally extended to any finite number of real arguments, this is used to establish functional relations between the parameters (``cascade relations''), relations between intersection exponent and halfspace exponents are established, new (consistent) conjectures for the values of intersection exponents for Brownian motion are formulated, new conjectures for the values of intersection exponents of loop-erased random walks are given. Since the publication of this paper the authors, together with O.~Schramm, have made considerable progress towards these and classical conjectures about the values of intersection exponents for Brownian motion.
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 81T40
zbMATH DE Number: 1496102
zbMATH Keywords: planar Brownian motion
zbMATH Keywords: intersection exponents
zbMATH Keywords: halfplane exponents
zbMATH Keywords: cascade relations
zbMATH Keywords: loop-erased random walk
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1022677543
OpenAlex ID: W4236972956
DOI: 10.1214/AOP/1022677543
description: scientific article; zbMATH DE number 1496102