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- W2949616295 abstract "For a symmetric random walk in $Z^2$ with $2+delta$ moments, we represent $|mathcal{R}(n)|$, the cardinality of the range, in terms of an expansion involving the renormalized intersection local times of a Brownian motion. We show that for each $kgeq 1$ [ (log n)^k [ frac{1}{n} |mathcal{R}(n)| +sum_{j=1}^k (-1)^j (textstyle{frac1{2pi}}log n +c_X)^{-j} gamma_{j,n}]to 0, qquad a.s. ] where $W_t$ is a Brownian motion, $W^{(n)}_t=W_{nt}/sqrt n$, $gamma_{j,n}$ is the renormalized intersection local time at time 1 for $W^{(n)}$, and $c_X$ is a constant depending on the distribution of the random walk." @default.
- W2949616295 created "2019-06-27" @default.
- W2949616295 creator A5033076994 @default.
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- W2949616295 date "2004-04-04" @default.
- W2949616295 modified "2023-09-27" @default.
- W2949616295 title "An almost sure invariance principle for the range of planar random walks" @default.
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