Capacity of the range of random walk on ℤ^{𝕕}

Asselah, Amine; Schapira, Bruno; Sousi, Perla

doi:10.1090/tran/7247

Capacity of the range of random walk on $\mathbb {Z}^d$
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by Amine Asselah, Bruno Schapira and Perla Sousi PDF

Trans. Amer. Math. Soc. 370 (2018), 7627-7645 Request permission

Abstract:

We study the capacity of the range of a transient simple random walk on $\mathbb {Z}^d$. Our main result is a central limit theorem for the capacity of the range for $d\ge 6$. We present a few open questions in lower dimensions.

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