## Abstract

In this note, we establish a functional central limit theorem for the capacity of the

range for a class of α-stable random walks on the integer lattice Z

range for a class of α-stable random walks on the integer lattice Z

^{d}with d > 5α/2. Using similar methods, we also prove an analogous result for the cardinality of the range when d > 3α/2.Original language | English |
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Number of pages | 12 |

Publication status | Published - 2019 |

### Publication series

Name | arXiv.org e-Print archive |
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Publisher | Cornell University Library |

## Keywords

- The range of a random walk
- Capacity
- Functional central limit theorem

## ASJC Scopus subject areas

- Mathematics(all)