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 math.CAShow all

45 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.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.CA2023

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

Pablo Shmerkin, Alexia Yavicoli

We prove that for $1 \leq k < d$ , if $E$ is a Borel subset of $R^{d}$ of Hausdorff dimension strictly larger than $k$ , the set of $(k + 1)$ -volumes determined by $k + 2$ points in $…

math.CA2023

On the Fourier decay of multiplicative convolutions

Tuomas Orponen, Nicolas de Saxcé, Pablo Shmerkin

We prove the following. Let $μ_{1}, \dots, μ_{n}$ be Borel probability measures on $[- 1, 1]$ such that $μ_{j}$ has finite $s_{j}$ -energy for certain indices $s_{j} \in (0, 1]$ with $s_{…

math.CA2023★ 1 cited

Inverse theorems for discretized sums and $L^{q}$ norms of convolutions in $R^{d}$

Pablo Shmerkin

We prove inverse theorems for the size of sumsets and the $L^{q}$ norms of convolutions in the discretized setting, extending to arbitrary dimension an earlier result of the author i…

Sharp Favard length of random Cantor sets

Full measure universality for Cantor Sets

Dynamical self-similarity, Lq-dimensions and Furstenberg slicing in Rd

On the volumes of simplices determined by a subset of Rd

On the Fourier decay of multiplicative convolutions

Inverse theorems for discretized sums and Lq norms of convolutions in Rd

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

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

Inverse theorems for discretized sums and $L^{q}$ norms of convolutions in $R^{d}$