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Local Central Limit Theorem for a Random Walk Perturbed in One Point

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Abstract

We consider a symmetric random walk on the ν-dimensional lattice, whose exit probability from the origin is modified by an antisymmetric perturbation and prove the local central limit theorem for this process. A short-range correction to diffusive behaviour appears in any dimension along with a long-range correction in the one-dimensional case.

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Acknowledgements

The authors thank C. Boldrighini for suggesting the problem. R. L. is supported by the ERC grant 676675 FLIRT.

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Correspondence to Giuseppe Genovese.

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Genovese, G., Lucà, R. Local Central Limit Theorem for a Random Walk Perturbed in One Point. Math Phys Anal Geom 22, 19 (2019). https://doi.org/10.1007/s11040-019-9316-6

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  • DOI: https://doi.org/10.1007/s11040-019-9316-6

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