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.
Publié le : 2011-02-15
Classification:
Simple random walk,
Winding number,
Averaged Dehn function,
52C45,
60D05
@article{1294170233,
author = {Schapira, Bruno and Young, Robert},
title = {Windings of planar random walks and averaged Dehn function},
journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
volume = {47},
number = {1},
year = {2011},
pages = { 130-147},
language = {en},
url = {http://dml.mathdoc.fr/item/1294170233}
}
Schapira, Bruno; Young, Robert. Windings of planar random walks and averaged Dehn function. Ann. Inst. H. Poincaré Probab. Statist., Tome 47 (2011) no. 1, pp. 130-147. http://gdmltest.u-ga.fr/item/1294170233/