Local Central Limit Theorem for a Random Walk Perturbed in One Point
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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.
KeywordsLocal central limit theorems Inhomogeneous random walks
Mathematics Subject Classification (2010)60F05 60G50 60J10
The authors thank C. Boldrighini for suggesting the problem. R. L. is supported by the ERC grant 676675 FLIRT.
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