8 papers
Self-affine sponges with random contractions
Balázs Bárány, Antti Käenmäki, Michał Rams
We compute the almost sure Hausdorff dimension of random self-affine sponges in without imposing any separation conditions. In this context, randomness arises from t…
Hausdorff measure of dominated planar self-affine sets with large dimension
Balázs Bárány
In this paper, we investigate the Hausdorff measure of planar dominated self-affine sets at their affinity dimension. We show that the Hausdorff measure being positive and finite i…
On the dimension theory of Okamoto's function
Balázs Bárány, R. Dániel Prokaj
In this paper, we investigate the dimension theory of the one parameter family of Okamoto's function. We compute the Hausdorff, box-counting and Assouad dimensions of the graph for…
Smoothness of random self-similar measures on the line and the existence of interior points
Balázs Bárány, Michał Rams
In this paper, we study the smoothness of the density function of absolutely continuous measures supported on random self-similar sets on the line. We show that the natural project…
Universal projection theorems with applications to multifractal analysis and the dimension of every ergodic measure on self-conformal sets simultaneously
Balázs Bárány, Károly Simon, Adam Śpiewak
We prove a universal projection theorem, giving conditions on a parametrized family of maps and a collection M of measures on X under which for almost eve…
Typical dimension and absolute continuity for classes of dynamically defined measures, Part II : exposition and extensions
Balázs Bárány, Károly Simon, Boris Solomyak +1
This paper is partly an exposition, and partly an extension of our work [1] to the multiparameter case. We consider certain classes of parametrized dynamically defined measures. Th…
On an abrasion motivated fractal model
Balázs Bárány, Gábor Domokos, Ágoston Szesztay
In this paper, we consider a fractal model motivated by the abrasion of convex polyhedra, where the abrasion is realised by chipping small neighbourhoods of vertices. After providi…
Level sets of prevalent Hölder functions
Roope Anttila, Balázs Bárány, Antti Käenmäki
We study the level sets of prevalent Hölder functions. For a prevalent -Hölder function on the unit interval, we show that the upper Minkowski dimension of every level set is bo…