92 citations · 502 across the 56 of their papers we have counts for
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Visible parts of fractal percolation
I. Arhosalo, E. Järvenpää, M. Järvenpää +2
We study dimensional properties of visible parts of fractal percolation in the plane. Provided that the dimension of the fractal percolation is at least 1, we show that, conditione…
Local entropy averages and projections of fractal measures
Michael Hochman, Pablo Shmerkin
We show that for families of measures on Euclidean space which satisfy an ergodic-theoretic form of "self-similarity" under the operation of re-scaling, the dimension of linear ima…
On the dimension of iterated sumsets
Jörg Schmeling, Pablo Shmerkin
Let A be a subset of the real line. We study the fractal dimensions of the k-fold iterated sumsets kA, defined as kA = A+...+A (k times). We show that for any non-decreasing sequen…
Convolutions of Cantor measures without resonance
Fedor Nazarov, Yuval Peres, Pablo Shmerkin
Denote by the distribution of the random sum , where and all the choices are independent. For , the measure…
The Hausdorff dimension of the projections of self-affine carpets
Andrew Ferguson, Thomas Jordan, Pablo Shmerkin
We study the orthogonal projections of a large class of self-affine carpets, which contains the carpets of Bedford and McMullen as special cases. Our main result is that if is…