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- W4327949730 abstract "Let (X,d) be a separable geodesic Gromov-hyperbolic space, o∈X a basepoint and μ a countably supported non-elementary probability measure on Isom(X). Denote by z n the random walk on X driven by the probability measure μ. Supposing that μ has a finite exponential moment, we give a second-order Taylor expansion of the large deviation rate function of the sequence 1 nd(z n ,o) and show that the corresponding coefficient is expressed by the variance in the central limit theorem satisfied by the sequence d(z n ,o). This provides a positive answer to a question raised in [6]. The proof relies on the study of the Laplace transform of d(z n ,o) at the origin using a martingale decomposition first introduced by Benoist–Quint together with an exponential submartingale transform and large deviation estimates for the quadratic variation process of certain martingales." @default.
- W4327949730 created "2023-03-21" @default.
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- W4327949730 date "2023-03-20" @default.
- W4327949730 modified "2023-10-07" @default.
- W4327949730 title "Random walks on hyperbolic spaces: second order expansion of the rate function at the drift" @default.
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- W4327949730 doi "https://doi.org/10.5802/jep.225" @default.
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