92 citations · 502 across the 56 of their papers we have counts for
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Self-similar measures: asymptotic bounds for the dimension and Fourier decay of smooth images
Carolina A. Mosquera, Pablo Shmerkin
R. Kaufman and M. Tsujii proved that the Fourier transform of self-similar measures has a power decay outside of a sparse set of frequencies. We present a version of this result fo…
Absolute continuity of non-homogeneous self-similar measures
Santiago Saglietti, Pablo Shmerkin, Boris Solomyak
We prove that self-similar measures on the real line are absolutely continuous for almost all parameters in the super-critical region, in particular confirming a conjecture of S-M.…
On the Hausdorff dimension of pinned distance sets
Pablo Shmerkin
We prove that if is a Borel set in the plane of equal Hausdorff and packing dimension , then the set of pinned distances has full Hausdorff dimension f…
Patterns in Random Fractals
Pablo Shmerkin, Ville Suomala
We characterize the existence of certain geometric configurations in the fractal percolation limit set in terms of the almost sure dimension of . Some examples of the config…
Hölder coverings of sets of small dimension
Eino Rossi, Pablo Shmerkin
We show that a set of small box counting dimension can be covered by a Hölder graph from all but a small set of directions, and give sharp bounds for the dimension of the exception…