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• W4309490407 abstract "We investigate the box-counting dimension of the image of a set $E subset mathbb{R}$ under a random multiplicative cascade function $f$. The corresponding result for Hausdorff dimension was established by Benjamini and Schramm in the context of random geometry, and for sufficiently regular sets, the same formula holds for the box-counting dimension. However, we show that this is far from true in general, and we compute explicitly a formula of a very different nature that gives the almost sure box-counting dimension of the random image $f(E)$ when the set $E$ comprises a convergent sequence. In particular, the box-counting dimension of $f(E)$ depends more subtly on $E$ than just on its dimensions. We also obtain lower and upper bounds for the box-counting dimension of the random images for general sets $E$." @default.
• W4309490407 created "2022-11-28" @default.
• W4309490407 creator A5022379865 @default.
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• W4309490407 date "2022-11-18" @default.
• W4309490407 modified "2023-10-17" @default.
• W4309490407 title "Box-Counting Dimension in One-Dimensional Random Geometry of Multiplicative Cascades" @default.
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• W4309490407 doi "https://doi.org/10.1007/s00220-022-04558-9" @default.
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