Adrien Boulanger
I2M, Aix-Marseille Université
/user/adrien.boulanger/
Date(s) : 17/04/2023 iCal
9 h 30 min - 11 h 30 min
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.
Emplacement
FRUMAM, St Charles (3ème étage)
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