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- W2951807215 abstract "Completing a strategy of Gouezel 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 $C R^{-n}n^{-3/2}$. 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." @default.
- W2951807215 created "2019-06-27" @default.
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- W2951807215 date "2012-09-14" @default.
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- W2951807215 title "Local limit theorem for symmetric random walks in Gromov-hyperbolic groups" @default.
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