Zobrazeno 1 - 10
of 74
pro vyhledávání: '"Järvenpää, Maarit"'
We consider the Hausdorff dimension of random covering sets generated by balls and general measures in Euclidean spaces. We prove, for a certain parameter range, a conjecture by Ekstr\"om and Persson concerning the exact value of the dimension in the
Externí odkaz:
http://arxiv.org/abs/2402.18289
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 set condition. The bound is valid for all visible parts and it depends
Externí odkaz:
http://arxiv.org/abs/2101.01017
We show that there exists $0<\alpha_0<1$ (depending on the parameters) such that the fractal percolation is almost surely purely $\alpha$-unrectifiable for all $\alpha>\alpha_0$.
Comment: After the referee's report a restructured more readable v
Comment: After the referee's report a restructured more readable v
Externí odkaz:
http://arxiv.org/abs/1910.11796
Publikováno v:
Math. Scand., 126(2), 2020, pp 229--255
The almost sure value of the Hausdorff dimension of limsup sets generated by randomly distributed rectangles in the Heisenberg group is computed in terms of directed singular value functions.
Comment: 21 pages
Comment: 21 pages
Externí odkaz:
http://arxiv.org/abs/1804.10405
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 function of the rectangles.
Comment: v2: Removed the subsection abo
Comment: v2: Removed the subsection abo
Externí odkaz:
http://arxiv.org/abs/1705.02616
Autor:
Järvenpää, Esa, Järvenpää, Maarit, Käenmäki, Antti, Rajala, Tapio, Rogovin, Sari, Suomala, Ville
Publikováno v:
Math. Z. 266 (2010), no. 1, 83-105
Let $X$ be a metric measure space with an $s$-regular measure $\mu$. We prove that if $A\subset X$ is $\varrho$-porous, then $\dim_{\mathrm{p}}(A)\le s-c\varrho^s$ where $\dim_{\mathrm{p}}$ is the packing dimension and $c$ is a positive constant whic
Externí odkaz:
http://arxiv.org/abs/1701.08593
Publikováno v:
Math. Scand. 97 (2005), no. 2, 309-318
In $\mathbb{R}^n$, we establish an asymptotically sharp upper bound for the upper Minkowski dimension of $k$-porous sets having holes of certain size near every point in $k$ orthogonal directions at all small scales. This bound tends to $n-k$ as $k$-
Externí odkaz:
http://arxiv.org/abs/1701.08584
Publikováno v:
In Advances in Mathematics 29 October 2021 390
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 spaces and in the $d$-dimensional torus. In metric spaces, we consider c
Externí odkaz:
http://arxiv.org/abs/1510.06630
We prove that for random affine code tree fractals the affinity dimension is almost surely equal to the unique zero of the pressure function. As a consequence, we show that the Hausdorff, packing and box counting dimensions of such systems are equal
Externí odkaz:
http://arxiv.org/abs/1510.02827