Pablo Shmerkin

activity

20042025

most citedLocal entropy averages and projections of fractal measures

92 citations · 502 across the 56 of their papers we have counts for

collaborators

Showing 2025Show all

3 papers · 1 filter

math.CA2025

Sharp Favard length of random Cantor sets

Alan Chang, Pablo Shmerkin, Ville Suomala

We show that for a large class of planar $1$ -dimensional random fractals $S$ , the Favard length $Fav (S (r))$ of the neighborhood $S (r)$ is comparable to $\log^{-1}(1/…

math.CA2025

Full measure universality for Cantor Sets

Pablo Shmerkin, Alexia Yavicoli

We investigate variants of the Erdős similarity problem for Cantor sets. We prove that under a mild Hausdorff or packing logarithmic dimension assumption, Cantor sets are not full…

math.PR2025

The largest slice of fractal percolation

Pablo Shmerkin, Ville Suomala

For each $k \geq 3$ , we determine the dimensional threshold for planar fractal percolation to contain $k$ collinear points. In the critical case of dimension $1$ , the largest linear…