3/2 et théorèmes limite local pour les marches aléatoires
Date(s) : 16/05/2023 iCal
9h30 - 11h30
Il y sera question du document :
LOCAL LIMIT THEOREM FOR SYMMETRIC RANDOM WALKS IN GROMOV-HYPERBOLIC GROUPS
par SÉBASTIEN GOUËZEL
JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, July 2014.
Completing a strategy of Gouëzel and Lalley, we prove a local limit theorem for the random walk generated by any symmetric finitely supported probability measure on a non-elementary Gromov-hyperbolic group: denoting by R the inverse of the spectral radius of the random walk, the probability to return to the identity at time n behaves like CR−nn−3/2. An important step in the proof is to extend Ancona’s results on the Martin boundary up to the spectral radius: we show that the Martin boundary for R-harmonic functions coincides with the geometric boundary of the group. In an appendix, we explain how the symmetry assumption of the measure can be dispensed with for surface groups.
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Emplacement
Saint-Charles - FRUMAM (3ème étage)
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