92 citations · 502 across the 56 of their papers we have counts for
5 papers · 1 filter
Spatially independent martingales, intersections, and applications
Pablo Shmerkin, Ville Suomala
We define a class of random measures, spatially independent martingales, which we view as a natural generalisation of the canonical random discrete set, and which includes as speci…
Squares and their centers
Tamás Keleti, Dániel T. Nagy, Pablo Shmerkin
We study the relationship between the sizes of two sets when contains either the whole boundary, or the four vertices, of a square with axes-parallel…
Absolute continuity of self-similar measures, their projections and convolutions
Pablo Shmerkin, Boris Solomyak
We show that in many parametrized families of self-similar measures, their projections, and their convolutions, the set of parameters for which the measure fails to be absolutely c…
On the dimensions of a family of overlapping self-affine carpets
Jonathan Fraser, Pablo Shmerkin
We consider the dimensions of a family of self-affine sets related to the Bedford-McMullen carpets. In particular, we fix a Bedford-McMullen system and then randomise the translati…
Dynamics of the scenery flow and geometry of measures
Antti Käenmäki, Tuomas Sahlsten, Pablo Shmerkin
We employ the ergodic theoretic machinery of scenery flows to address classical geometric measure theoretic problems on Euclidean spaces. Our main results include a sharp version o…