### Abstract

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 |
---|---|

Number of pages | 12 |

Journal | arXiv.org e-Print archive |

Publication status | Published - 2019 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*arXiv.org e-Print archive*.

**Functional CLT for the range of stable random walks.** / Cygan, Wojciech; Sandrić, Nikola; Sebek, Stjepan.

Research output: Contribution to journal › Article › Research

*arXiv.org e-Print archive*.

}

TY - JOUR

T1 - Functional CLT for the range of stable random walks

AU - Cygan, Wojciech

AU - Sandrić, Nikola

AU - Sebek, Stjepan

PY - 2019

Y1 - 2019

N2 - In this note, we establish a functional central limit theorem for the capacity of therange for a class of α-stable random walks on the integer lattice Zd with d > 5α/2. Using similar methods, we also prove an analogous result for the cardinality of the range when d > 3α/2.

AB - In this note, we establish a functional central limit theorem for the capacity of therange for a class of α-stable random walks on the integer lattice Zd with d > 5α/2. Using similar methods, we also prove an analogous result for the cardinality of the range when d > 3α/2.

KW - The range of a random walk

KW - Capacity

KW - Functional central limit theorem

M3 - Article

JO - arXiv.org e-Print archive

JF - arXiv.org e-Print archive

ER -