Zobrazeno 1 - 10
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pro vyhledávání: '"Báràny, P."'
Autor:
Bárány, Imre
In a vector balancing game, on step $k$ player 1 chooses a unit vector $v_k$ and player 2 chooses a sign $\varepsilon_k\in \{-1,1\}$, and the position after $n$ steps is $z_n=\sum_1^n\varepsilon_k v_k$. Player 1's target is to make $\|z_n\|$ large an
Externí odkaz:
http://arxiv.org/abs/2412.08238
Autor:
Bárány, Balázs, Rams, Michał
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 projection of a measure with symbolic local dimension greater than 1 at every
Externí odkaz:
http://arxiv.org/abs/2412.06008
We prove a universal projection theorem, giving conditions on a parametrized family of maps $\Pi_\lambda : X \to \mathbb{R}^d$ and a collection $M$ of measures on $X$ under which for almost every $\lambda$ equality $\mathrm{dim}_H \Pi_\lambda \mu = \
Externí odkaz:
http://arxiv.org/abs/2412.03529
Assume two finite families $\mathcal A$ and $\mathcal B$ of convex sets in $\mathbb{R}^3$ have the property that $A\cap B\ne \emptyset$ for every $A \in \mathcal A$ and $B\in \mathcal B$. Is there a constant $\gamma >0$ (independent of $\mathcal A$ a
Externí odkaz:
http://arxiv.org/abs/2409.06472
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. These are push-forwards, under the natural projection, of ergodic measur
Externí odkaz:
http://arxiv.org/abs/2405.06466
Autor:
Katranidis, Vasileios, Barany, Gabor
The demand for accurate and efficient verification of information in texts generated by large language models (LMs) is at an all-time high, but remains unresolved. Recent efforts have focused on extracting and verifying atomic facts from these texts
Externí odkaz:
http://arxiv.org/abs/2403.03888
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 providing a formal description of the successive chippings, we show that the
Externí odkaz:
http://arxiv.org/abs/2402.17765
We study the level sets of prevalent H\"older functions. For a prevalent $\alpha$-H\"older function on the unit interval, we show that the upper Minkowski dimension of every level set is bounded from above by $1-\alpha$ and Lebesgue positively many l
Externí odkaz:
http://arxiv.org/abs/2402.08520
Autor:
Bárány, Imre, Domokos, Gábor
Given a polytope $P\subset R^3$ and a non-zero vector $z \in R^3$, the plane $\{x\in R^3:zx=t\}$ intersects $P$ in convex polygon $P(z,t)$ for $t \in [t^-,t^+]$ where $t^-=\min \{zx: x \in P\}$ and $t^+=\max \{zx: x\in P\}$, $zx$ is the scalar produc
Externí odkaz:
http://arxiv.org/abs/2310.18960
We show that any self-conformal measure $\mu$ on $\mathbb{R}$ is uniformly scaling and generates an ergodic fractal distribution. This generalizes existing results by removing the need for any separation condition. We also obtain applications to the
Externí odkaz:
http://arxiv.org/abs/2308.11399