Windings of planar random walks and averaged Dehn function
Annales de l'I.H.P. Probabilités et statistiques, Volume 47 (2011) no. 1, p. 130-147

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.

Le principal résultat de cet article donne un équivalent précis de l'espérance du nombre total de tours effectués par la marche aléatoire simple sur ℤ2 ou sur le réseau triangulaire. Comme corollaire, nous obtenons une nouvelle borne inférieure de la fonction de Dehn moyennée sur ℤd, d ≥ 2, qui mesure l'aire moyenne du disque remplissant de manière optimale une courbe de longueur donnée.

DOI : https://doi.org/10.1214/10-AIHP365
Classification:  52C45,  60D05
Keywords: simple random walk, winding number, averaged Dehn function
@article{AIHPB_2011__47_1_130_0,
     author = {Schapira, Bruno and Young, Robert},
     title = {Windings of planar random walks and averaged Dehn function},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {47},
     number = {1},
     year = {2011},
     pages = {130-147},
     doi = {10.1214/10-AIHP365},
     zbl = {pre05864078},
     mrnumber = {2779400},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2011__47_1_130_0}
}
Schapira, Bruno; Young, Robert. Windings of planar random walks and averaged Dehn function. Annales de l'I.H.P. Probabilités et statistiques, Volume 47 (2011) no. 1, pp. 130-147. doi : 10.1214/10-AIHP365. http://www.numdam.org/item/AIHPB_2011__47_1_130_0/

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