Pablo Shmerkin

collaborators

4 papers

math.CA2026

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.CA2026

Projections, Furstenberg sets, and the $A B C$ sum-product problem

Tuomas Orponen, Pablo Shmerkin

We make progress on two interrelated problems at the intersection of geometric measure theory, additive combinatorics and harmonic analysis: the discretised sum-product problem, an…

math.CA2025

Full measure universality for Cantor Sets

Pablo Shmerkin, Alexia Yavicoli

We investigate variants of the ErdÅs 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…

Sharp Favard length of random Cantor sets

Projections, Furstenberg sets, and the ABC sum-product problem

Full measure universality for Cantor Sets

The largest slice of fractal percolation

Projections, Furstenberg sets, and the $A B C$ sum-product problem