Windings of planar random walks and averaged Dehn function

Bruno Schapira; Robert Young

doi:10.1214/10-AIHP365

Windings of planar random walks and averaged Dehn function

Bruno Schapira, Robert Young

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We prove sharp estimates on the expected number of windings of a simple random walk on the square or triangular lattice. This gives new lower bounds on the averaged Dehn function, which measures the expected area needed to fill a random curve with a disc.

Original language	English (US)
Pages (from-to)	130-147
Number of pages	18
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	47
Issue number	1
DOIs	https://doi.org/10.1214/10-AIHP365
State	Published - Feb 2011

Keywords

Averaged Dehn function
Simple random walk
Winding number

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/10-AIHP365

Cite this

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abstract = "We prove sharp estimates on the expected number of windings of a simple random walk on the square or triangular lattice. This gives new lower bounds on the averaged Dehn function, which measures the expected area needed to fill a random curve with a disc.",

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Windings of planar random walks and averaged Dehn function

Abstract

Keywords

ASJC Scopus subject areas

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