92 citations · 502 across the 56 of their papers we have counts for
4 papers · 1 filter
On Furstenberg's intersection conjecture, self-similar measures, and the norms of convolutions
Pablo Shmerkin
We study a class of measures on the real line with a kind of self-similar structure, which we call dynamically driven self-similar measures, and contain proper self-similar measure…
On distance sets, box-counting and Ahlfors-regular sets
Pablo Shmerkin
We obtain box-counting estimates for the pinned distance sets of (dense subsets of) planar discrete Ahlfors-regular sets of exponent . As a corollary, we improve upon a recent…
A class of random Cantor measures, with applications
Pablo Shmerkin, Ville Suomala
We survey some of our recent results on the geometry of spatially independent martingales, in a more concrete setting that allows for shorter, direct proofs, yet is general enough…
On equality of Hausdorff and affinity dimensions, via self-affine measures on positive subsystems
Ian D. Morris, Pablo Shmerkin
Under mild conditions we show that the affinity dimension of a planar self-affine set is equal to the supremum of the Lyapunov dimensions of self-affine measures supported on self-…