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

collaborators

34 papers

quant-ph2026

Beyond Gaussian Entanglement: Practical Criteria for Polynomially Excited Quantum States

Gábor Homa, Richárd Balka, Nikolett Német +3

Polynomial excitations consisting of creation and annihilation operators are studied. Subsystem entanglement is proven produced and preserved by such manipulations. NPT entanglemen…

math.CA2025

Signed null sequences and Hausdorff dimension

Richárd Balka, Kornélia Héra, Gergely Kiss

We investigate the convergence of signed null sequences of the form \[ \sum_{n=1}^\infty \varepsilon_n a_n, \quad \varepsilon_n \in \{-1,1\}, \] where $(a_{n})$ tends to zero in $\ma…

math.MG2024

On the uniformity and size of microsets

Richárd Balka, Vilma Orgoványi, Alex Rutar

We resolve a few questions regarding the uniformity and size of microsets of subsets of Euclidean space. First, we construct a compact set $K \subset R^{d}$ with Assouad dimen…

quant-ph2024

Effective eigenvalue approximation from moments for self-adjoint trace-class operators

Richárd Balka, Gábor Homa, András Csordás

Spectral properties of bounded linear operators play a crucial role in several areas of mathematics and physics. For each self-adjoint, trace-class operator $O$ we define a set $Λ_…

quant-ph2024★ 2 cited

Positivity and entanglement of polynomial Gaussian integral operators

Richárd Balka, András Csordás, Gábor Homa

Positivity preservation is an important issue in the dynamics of open quantum systems: positivity violations always mark the border of validity of the model. We investigate the pos…

math.CA2023

New Hausdorff type dimensions and optimal bounds for bilipschitz invariant dimensions

Richárd Balka, Tamás Keleti

We introduce a new family of fractal dimensions by restricting the set of diameters in the coverings in the usual definition of the Hausdorff dimension. Among others, we prove that…

math.CA2023

Lipschitz images and dimensions

Richárd Balka, Tamás Keleti

We consider the question which compact metric spaces can be obtained as a Lipschitz image of the middle third Cantor set, or more generally, as a Lipschitz image of a subset of a g…

quant-ph2022★ 3 cited

Newton's identities and positivity of trace class integral operators

G. Homa, R. Balka, J. Z. Bernád +2

We provide a countable set of conditions based on elementary symmetric polynomials that are necessary and sufficient for a trace class integral operator to be positive semidefinite…

math.CA2021★ 1 cited

Stability and measurability of the modified lower dimension

Richárd Balka, Márton Elekes, Viktor Kiss

The lower dimension $dim_{L}$ is the dual concept of the Assouad dimension. As it fails to be monotonic, Fraser and Yu introduced the modified lower dimension $dim_{M L}$ by making…

math.CA2021

The range of dimensions of microsets

Richárd Balka, Márton Elekes, Viktor Kiss

We say that $E$ is a microset of the compact set $K \subset R^{d}$ if there exist sequences $λ_{n} \geq 1$ and $u_{n} \in R^{d}$ such that $(λ_{n} K + u_{n}) \cap [0, 1]^{d}$ conv…

math.CA2020

Singularity of maps of several variables and a problem of Mycielski concerning prevalent homeomorphisms

Richárd Balka, Márton Elekes, Viktor Kiss +1

S. Banach pointed out that the graph of the generic (in the sense of Baire category) element of $Homeo ([0, 1])$ has length $2$ . J. Mycielski asked if the measure theoretic du…

math.CA2020

Compact sets with large projections and nowhere dense sumset

Richárd Balka, Márton Elekes, Viktor Kiss +2

We answer a question of Banakh, Jabłońska and Jabłoński by showing that for $d \geq 2$ there exists a compact set $K \subseteq R^{d}$ such that the projection of $K$ onto each…

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.CA2016

Dimensions of fibers of generic continuous maps

Richárd Balka

In an earlier paper Buczolich, Elekes and the author described the Hausdorff dimension of the level sets of a generic real-valued continuous function (in the sense of Baire categor…

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.CA2015

Dimensions of graphs of prevalent continuous maps

Richárd Balka

Let $K$ be an uncountable compact metric space and let $C (K, R^{d})$ denote the set of continuous maps $f : K \to R^{d}$ endowed with the maximum norm. The goal of…

math.CA2014

Hausdorff and packing dimension of fibers and graphs of prevalent continuous maps

Richárd Balka, Udayan B. Darji, Márton Elekes

The notions of shyness and prevalence generalize the property of being zero and full Haar measure to arbitrary (not necessarily locally compact) Polish groups. The main goal of the…

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…

math.CA2013★ 9 cited

Bruckner--Garg-type results with respect to Haar null sets in $C [0, 1]$

Richárd Balka, Udayan B. Darji, Márton Elekes

A set $A \subset C [0, 1]$ is \emph{shy} or \emph{Haar null } (in the sense of Christensen) if there exists a Borel set $B \subset C [0, 1]$ and a Borel probability m…

math.CA2012★ 1 cited

Inductive topological Hausdorff dimensions and fibers of generic continuous functions

Richárd Balka

In an earlier paper Buczolich, Elekes and the author introduced a new concept of dimension for metric spaces, the so called topological Hausdorff dimension. They proved that it is…

math.CA2012

Answer to a question of Kolmogorov

Richárd Balka, Márton Elekes, András Máthé

More than 80 years ago Kolmogorov asked the following question. Let $E \subseteq R^{2}$ be a measurable set with $λ^{2} (E) < \infty$ , where $λ^{2}$ denotes the two-dimensional…

Beyond Gaussian Entanglement: Practical Criteria for Polynomially Excited Quantum States

Signed null sequences and Hausdorff dimension

On the uniformity and size of microsets

Effective eigenvalue approximation from moments for self-adjoint trace-class operators

Positivity and entanglement of polynomial Gaussian integral operators

New Hausdorff type dimensions and optimal bounds for bilipschitz invariant dimensions

Lipschitz images and dimensions

Newton's identities and positivity of trace class integral operators

Stability and measurability of the modified lower dimension

The range of dimensions of microsets

Singularity of maps of several variables and a problem of Mycielski concerning prevalent homeomorphisms

Compact sets with large projections and nowhere dense sumset

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

Baum-Katz type theorems with exact threshold

Dimensions of fibers of generic continuous maps

Uniform dimension results for fractional Brownian motion

Restrictions of Hölder continuous functions

Dimensions of graphs of prevalent continuous maps

Hausdorff and packing dimension of fibers and graphs of prevalent continuous maps

Increasing subsequences of random walks

Restrictions of Brownian motion

Bruckner--Garg-type results with respect to Haar null sets in C[0,1]

Inductive topological Hausdorff dimensions and fibers of generic continuous functions

Answer to a question of Kolmogorov

Bruckner--Garg-type results with respect to Haar null sets in $C [0, 1]$