On P\'olya's random walk constants
| Autor: | Gaunt, Robert E., Nadarajah, Saralees, Pogány, Tibor K. |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | A celebrated result in probability theory is that a simple symmetric random walk on the $d$-dimensional lattice $\mathbb{Z}^d$ is recurrent for $d=1,2$ and transient for $d\geq 3$. In this note, we derive a closed-form expression, in terms of the Lauricella function $F_C$, for the return probability for all $d\geq3$. Previously, a closed-form formula had only been available for $d=3$. Comment: 5 pages |
| Databáze: | arXiv |
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