44 citations · 175 across the 26 of their papers we have counts for
35 papers
New bounds on Cantor maximal operators
Pablo Shmerkin, Ville Suomala
We prove bounds for the maximal operators associated to an Ahlfors-regular variant of fractal percolation. Our bounds improve upon those obtained by I. Łaba and M. Pramanik a…
Random perfect information games
János Flesch, Arkadi Predtetchinski, Ville Suomala
The paper proposes a natural measure space of zero-sum perfect information games with upper semicontinuous payoffs. Each game is specified by the game tree, and by the assignment o…
On dimensions of visible parts of self-similar sets with finite rotation groups
Esa Järvenpää, Maarit Järvenpää, Ville Suomala +1
We derive an upper bound for the Assouad dimension of visible parts of self-similar sets generated by iterated function systems with finite rotation groups and satisfying the open…
Covering the Sierpiński carpet with tubes
Aleksi Pyörälä, Pablo Shmerkin, Ville Suomala +1
We show that non-trivial -invariant sets in , such as the Sierpiński carpet and the Sierpiński sponge, are tube-null, that is, they can be covered by a union of…
Intermediate value property for the Assouad dimension of measures
Ville Suomala
Hare, Mendivil, and Zuberman have recently shown that if is a compact subset of the reals and of non-zero Assouad dimension , then for all , supports…
The doubling metric and doubling measures
János Flesch, Arkadi Predtetchinski, Ville Suomala
We introduce the so--called doubling metric on the collection of non--empty bounded open subsets of a metric space. Given a subset of a metric space , the predecessor $U_{*}…
Fractal percolation and quasisymmetric mappings
Eino Rossi, Ville Suomala
We study the conformal dimension of fractal percolation and show that, almost surely, the conformal dimension of a fractal percolation is strictly smaller than its Hausdorff dimens…
Projections of Poisson cut-outs in the Heisenberg group and the visual -sphere
Laurent Dufloux, Ville Suomala
We study projectional properties of Poisson cut-out sets in non-Euclidean spaces. In the first Heisenbeg group, endowed with the Korányi metric, we show that the Hausdorff dime…
Hausdorff dimension of limsup sets of random rectangles in products of regular spaces
Fredrik Ekström, Esa Järvenpää, Maarit Järvenpää +1
The almost sure Hausdorff dimension of the limsup set of randomly distributed rectangles in a product of Ahlfors regular metric spaces is computed in terms of the singular value fu…
Patterns in Random Fractals
Pablo Shmerkin, Ville Suomala
We characterize the existence of certain geometric configurations in the fractal percolation limit set in terms of the almost sure dimension of . Some examples of the config…
Upper Conical density results for general measures on
Marianna Csörnyei, Antti Käenmäki, Tapio Rajala +1
We study conical density properties of general Borel measures on Euclidean spaces. Our results are analogous to the previously known result on the upper density properties of Hausd…
Packing dimension and Ahlfors regularity of porous sets in metric spaces
Esa Järvenpää, Maarit Järvenpää, Antti Käenmäki +3
Let be a metric measure space with an -regular measure . We prove that if is -porous, then where $\dim_{\math…
Conical upper density theorems and porosity of measures
Antti Käenmäki, Ville Suomala
We study how measures with finite lower density are distributed around -planes in small balls in . We also discuss relations between conical upper density theo…
Asymptotically sharp dimension estimates for -porous sets
Esa Järvenpää, Maarit Järvenpää, Antti Käenmäki +1
In , we establish an asymptotically sharp upper bound for the upper Minkowski dimension of -porous sets having holes of certain size near every point in orthog…
A class of random Cantor measures, with applications
Pablo Shmerkin, Ville Suomala
We survey some of our recent results on the geometry of spatially independent martingales, in a more concrete setting that allows for shorter, direct proofs, yet is general enough…
Hitting probabilities of random covering sets in tori and metric spaces
Esa Järvenpää, Maarit Järvenpää, Henna Koivusalo +3
We provide sharp lower and upper bounds for the Hausdorff dimension of the intersection of a typical random covering set with a fixed analytic set both in Ahlfors regular metric sp…
Dimensions of random covering sets in Riemann manifolds
De-Jun Feng, Esa Järvenpää, Maarit Järvenpää +1
Let , and be -dimensional Riemann manifolds. Assume that is a sequence of Lebesgue measurable subsets of ${\pmb M…
Fractal percolation, porosity, and dimension
Changhao Chen, Tuomo Ojala, Eino Rossi +1
We study the porosity properties of fractal percolation sets . Among other things, for all , we obtain dimension bounds for the set of…
Local dimensions in Moran constructions
Antti Käenmäki, Bing Li, Ville Suomala
We study the dimensional properties of Moran sets and Moran measures in doubling metric spaces. In particular, we consider local dimensions and -dimensions. We generalize and…
Random cutout sets with spatially inhomogeneous intensities
Tuomo Ojala, Ville Suomala, Meng Wu
We study the Hausdorff dimension of Poissonian cutout sets defined via inhomogeneous intensity measures on Ahlfors-regular metric spaces. We obtain formulas for the Hausdorff dimen…
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…
Projections of random covering sets
Changhao Chen, Henna Koivusalo, Bing Li +1
We show that, almost surely, the Hausdorff dimension of a random covering set is preserved under all orthogonal projections to linear subspaces with dimension . The re…
A note on the hitting probabilities of random covering sets
Bing Li, Ville Suomala
Let be the random covering set on the torus , where is a sequence of ball-like sets and is a sequence of inde…
Local multifractal analysis in metric spaces
Antti Käenmäki, Tapio Rajala, Ville Suomala
We study the local dimensions and local multifractal properties of measures on doubling metric spaces. Our aim is twofold. On one hand, we show that there are plenty of multifracta…