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

69 papers

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…

math.CA2024

Dynamical self-similarity, $L^{q}$ -dimensions and Furstenberg slicing in $R^{d}$

Emilio Corso, Pablo Shmerkin

We extend a theorem of the second author on the $L^{q}$ -dimensions of dynamically driven self-similar measures from the real line to arbitrary dimension. Our approach provides a nove…

math.DS2024

On the dimension of orthogonal projections of self-similar measures

Amir Algom, Pablo Shmerkin

Let $ν$ be a self similar measure on $R^{d}$ , $d \geq 2$ , and let $π$ be an orthogonal projection onto a $k$ -dimensional subspace. We formulate a criterion on the action of t…

math.CA2023

On the volumes of simplices determined by a subset of $R^{d}$