Windings of planar random walks and averaged Dehn function

Bruno Schapira, Robert Young

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)130-147
Number of pages18
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Issue number1
StatePublished - Feb 2011


  • Averaged Dehn function
  • Simple random walk
  • Winding number

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


Dive into the research topics of 'Windings of planar random walks and averaged Dehn function'. Together they form a unique fingerprint.

Cite this