Windings of planar random walks and averaged Dehn function

Bruno Schapira (1) , Robert Young (2)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 IHES - Institut des Hautes Études Scientifiques

We prove a sharp estimate on the expected value of the integral of the index 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.

Mots clés: simple random walk; winding number; averaged Dehn function

Domaines: Probabilités [math.PR]; Topologie géométrique [math.GT]; Théorie des groupes [math.GR]

Bruno Schapira, Robert Young. Windings of planar random walks and averaged Dehn function. 2009. ⟨hal-00296638v3⟩