R. Balka

activity

20112026

most citedTopological Hausdorff dimension and level sets of generic continuous functions on fractals

30 citations · 63 across the 24 of their papers we have counts for

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6 papers · 1 filter

math.PR2016

Packing dimension of images and graphs of Gaussian random fields with drift

Richárd Balka

Let $X = {(X_{1} (t), \dots, X_{d} (t)) : t \in R^{n}}$ be a Gaussian random field in $R^{d}$ such that $X_{1}, \dots, X_{d}$ are independent, centered Gaussian random fields with co…

math.PR2016

Baum-Katz type theorems with exact threshold

Richárd Balka, Tibor Tómács

Let ${X_{n}}_{n \geq 1}$ be either a sequence of arbitrary random variables, or a martingale difference sequence, or a centered sequence with a suitable level of negative dependence…

math.PR2015

Uniform dimension results for fractional Brownian motion

Richárd Balka, Yuval Peres

Kaufman's dimension doubling theorem states that for a planar Brownian motion ${B (t) : t \in [0, 1]}$ we have $$\mathbb{P}(\dim \mathbf{B}(A)=2\dim A \textrm{ for all } A\s…

math.PR2015

Restrictions of Hölder continuous functions

Omer Angel, Richárd Balka, András Máthé +1

For $0 < α < 1$ let $V (α)$ denote the supremum of the numbers $v$ such that every $α$ -Hölder continuous function is of bounded variation on a set of Hausdorff dimension $v$ . Kahane and…

math.PR2014★ 7 cited

Increasing subsequences of random walks

Omer Angel, Richárd Balka, Yuval Peres

Given a sequence of $n$ real numbers ${S_{i}}_{i \leq n}$ , we consider the longest weakly increasing subsequence, namely $i_{1} < i_{2} < \dots < i_{L}$ with $S_{i_{k}} \leq S_{i_{k + 1}}$ and $L$ …

math.PR2014★ 7 cited

Restrictions of Brownian motion

Richárd Balka, Yuval Peres

Let ${B (t) : 0 \leq t \leq 1}$ be a linear Brownian motion and let $dim$ denote the Hausdorff dimension. Let $α > \frac{1}{2}$ and $1 \leq β \leq 2$ . We prove that, almost surely, t…