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

  • Giuseppe GenoveseEmail author
  • Renato Lucà
Article
  • 46 Downloads

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.

Keywords

Local central limit theorems Inhomogeneous random walks 

Mathematics Subject Classification (2010)

60F05 60G50 60J10 

Notes

Acknowledgements

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

References

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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Institut für MathematikUniversität ZürichZürichSwitzerland
  2. 2.Departement Mathematik und InformatikUniversität BaselBaselSwitzerland

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