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Limit law for the cover time of a random walk on a binary tree
Amir Demboa, Jay Rosenb c, Ofer Zeitounid e
- aDepartment of Mathematics & Department of Statistics, Stanford University, Stanford, CA 94305, USA
- bDepartment of Mathematics, College of Staten Island, CUNY, Staten Island, NY 10314, USA
- cDepartment of Mathematics, College of Staten Island, Cuny, Staten Island, NY 10314 USA
- dFaculty of Mathematics, Weitzmann Institute, Rehovot 76100, Israel
- eCourant Institute, NYU, New York, NY 10012, USA
Annales de l Institut Henri Poincaré Probabilités et StatistiquesInstitute of Mathematical Statistics2021-05-01 7 citations32 references
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Abstract
Let Tn denote the binary tree of depth n augmented by an extra edge connected to its root. Let Cn denote the cover time of Tn by simple random walk. We prove that the sequence of random variables Cn 2−(n+1)−mn, where mn is an explicit constant, converges in distribution as n→∞, and identify the limit.