The Brownian web is a two-dimensional black noise

Tom Ellis, Ohad N. Feldheim

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

The Brownian web is a random variable consisting of a Brownian motion starting from each space-time point on the plane. These are independent until they hit each other, at which point they coalesce. Tsirelson mentions this model in (Scaling Limit, Noise, Stability (2004) Springer), along with planar percolation, in suggesting the existence of a two-dimensional black noise. A two-dimensional noise is, roughly speaking, a random object on the plane whose distribution is translation invariant and whose behavior on disjoint subsets is independent. Black means sensitive to the resampling of sets of arbitrarily small total area. Tsirelson implicitly asks: "Is the Brownian web a two-dimensional black noise?." We give a positive answer to this question, providing the second known example of such after the scaling limit of critical planar percolation.

Original languageAmerican English
Pages (from-to)162-172
Number of pages11
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Volume52
Issue number1
DOIs
StatePublished - Feb 2016
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2016 Association des Publications de l'Institut Henri Poincare.

Keywords

  • Black noise
  • Brownian web

Fingerprint

Dive into the research topics of 'The Brownian web is a two-dimensional black noise'. Together they form a unique fingerprint.

Cite this