@article{MTMT:34126755,
	title = {Compact sets with large projections and nowhere dense sumset},
	url = {https://m2.mtmt.hu/api/publication/34126755},
	author = {Balka, Richárd and Elekes, Márton and Kiss, Viktor and Nagy, Donát and Poór, Márk},
	doi = {10.1088/1361-6544/acebae},
	journal-iso = {NONLINEARITY},
	journal = {NONLINEARITY},
	volume = {36},
	unique-id = {34126755},
	issn = {0951-7715},
	abstract = {We answer a question of Banakh, Jabłońska and Jabłoński by showing that for d ⩾ 2 there exists a compact set K ⊆ R d such that the projection of K onto each hyperplane is of non-empty interior, but K  +  K is nowhere dense. The proof relies on a random construction. A natural approach in the proofs is to construct such a K in the unit cube with full projections, that is, such that the projections of K agree with that of the unit cube. We investigate the generalization of these problems for projections onto various dimensional subspaces as well as for ℓ -fold sumsets. We obtain numerous positive and negative results, but also leave open many interesting cases. We also show that in most cases if we have a specific example of such a compact set then actually the generic (in the sense of Baire category) compact set in a suitably chosen space is also an example. Finally, utilizing a computer-aided construction, we show that the compact set in the plane with full projections and nowhere dense sumset can be self-similar.},
	year = {2023},
	eissn = {1361-6544},
	pages = {5190-5215},
	orcid-numbers = {Elekes, Márton/0000-0002-5139-2169}
}

@article{MTMT:33720054,
	title = {Newton’s identities and positivity of trace class integral operators},
	url = {https://m2.mtmt.hu/api/publication/33720054},
	author = {Homa, Gábor and Balka, Richárd and Bernád, J.Z. and Károly, M. and Csordás, András},
	doi = {10.1088/1751-8121/acc147},
	journal-iso = {J PHYS A-MATH THEOR},
	journal = {JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL},
	volume = {56},
	unique-id = {33720054},
	issn = {1751-8113},
	year = {2023},
	eissn = {1751-8121},
	orcid-numbers = {Homa, Gábor/0000-0001-9806-7358; Csordás, András/0000-0001-6530-2008}
}

@article{MTMT:32734627,
	title = {Stability and measurability of the modified lower dimension},
	url = {https://m2.mtmt.hu/api/publication/32734627},
	author = {Balka, Richárd and Elekes, Márton and Kiss, Viktor},
	doi = {10.1090/proc/16029},
	journal-iso = {P AM MATH SOC},
	journal = {PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY},
	volume = {150},
	unique-id = {32734627},
	issn = {0002-9939},
	abstract = {The lower dimension dimL is the dual concept of the Assouad dimension. As it fails to be monotonic, Fraser and Yu introduced the modified lower dimension dimML by making the lower dimension monotonic with the simple formula dimMLX=sup{dimLE:E⊂X}.
		As our first result we prove that the modified lower dimension is finitely stable in any metric space, answering a question of Fraser and Yu.
		We prove a new, simple characterization for the modified lower dimension. For a metric space X let K(X) denote the metric space of the non-empty compact subsets of X endowed with the Hausdorff metric. As an application of our characterization, we show that the map dimML:K(X)→[0,∞] is Borel measurable. More precisely, it is of Baire class 2, but in general not of Baire class 1. This answers another question of Fraser and Yu.
		Finally, we prove that the modified lower dimension is not Borel measurable defined on the closed sets of ℓ1 endowed with the Effros Borel structure.},
	year = {2022},
	eissn = {1088-6826},
	pages = {3889-3898},
	orcid-numbers = {Elekes, Márton/0000-0002-5139-2169}
}

@article{MTMT:32012587,
	title = {Singularity of maps of several variables and a problem of Mycielski concerning prevalent homeomorphisms},
	url = {https://m2.mtmt.hu/api/publication/32012587},
	author = {Balka, Richárd and Elekes, Márton and Kiss, Viktor and Poór, Márk},
	doi = {10.1016/j.aim.2021.107773},
	journal-iso = {ADV MATH},
	journal = {ADVANCES IN MATHEMATICS},
	volume = {385},
	unique-id = {32012587},
	issn = {0001-8708},
	year = {2021},
	eissn = {1090-2082},
	orcid-numbers = {Elekes, Márton/0000-0002-5139-2169}
}

@article{MTMT:3340900,
	title = {Restrictions of Hölder continuous functions},
	url = {https://m2.mtmt.hu/api/publication/3340900},
	author = {Omer, Angel and Balka, Richárd and Máthé, András and Yuval, Peres},
	doi = {10.1090/tran/7126},
	journal-iso = {T AM MATH SOC},
	journal = {TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY},
	volume = {370},
	unique-id = {3340900},
	issn = {0002-9947},
	year = {2018},
	eissn = {1088-6850},
	pages = {4223-4247}
}

@article{MTMT:3260290,
	title = {Baum-Katz type theorems with exact threshold},
	url = {https://m2.mtmt.hu/api/publication/3260290},
	author = {Balka, Richárd and Tómács, Tibor},
	doi = {10.1080/17442508.2017.1366490},
	journal-iso = {STOCHASTICS},
	journal = {STOCHASTICS},
	volume = {90},
	unique-id = {3260290},
	issn = {1744-2508},
	keywords = {Independent random variables; Complete convergence; rate of convergence; martingale difference sequences; Marcinkiewicz–Zygmund strong law of large numbers},
	year = {2018},
	eissn = {1744-2516},
	pages = {473-503}
}

@article{MTMT:3338647,
	title = {Uniform dimension results for fractional Brownian motion},
	url = {https://m2.mtmt.hu/api/publication/3338647},
	author = {Balka, Richárd and Peres, Y},
	doi = {10.4171/JFG/48},
	journal-iso = {J FRACTAL GEOM},
	journal = {JOURNAL OF FRACTAL GEOMETRY},
	volume = {4},
	unique-id = {3338647},
	issn = {2308-1309},
	year = {2017},
	eissn = {2308-1317},
	pages = {147-183}
}

@article{MTMT:3278973,
	title = {Dimensions of fibers of generic continuous maps},
	url = {https://m2.mtmt.hu/api/publication/3278973},
	author = {Balka, Richárd},
	doi = {10.1007/s00605-017-1067-5},
	journal-iso = {MONATSH MATH},
	journal = {MONATSHEFTE FUR MATHEMATIK},
	volume = {184},
	unique-id = {3278973},
	issn = {0026-9255},
	abstract = {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 category) defined on a compact metric space K by introducing the notion of topological Hausdorff dimension. Later on, the author extended the theory for maps from K to (Formula presented.). The main goal of this paper is to generalize the relevant results for topological and packing dimensions and to obtain new results for sufficiently homogeneous spaces K even in the case case of Hausdorff dimension. Let K be a compact metric space and let us denote by (Formula presented.) the set of continuous maps from K to (Formula presented.) endowed with the maximum norm. Let (Formula presented.) be one of the topological dimension (Formula presented.), the Hausdorff dimension (Formula presented.), or the packing dimension (Formula presented.). Define (Formula presented.)We prove that (Formula presented.) is the right notion to describe the dimensions of the fibers of a generic continuous map (Formula presented.). In particular, we show that (Formula presented.) provided that (Formula presented.), otherwise every fiber is finite. Proving the above theorem for packing dimension requires entirely new ideas. Moreover, we show that the supremum is attained on the left hand side of the above equation. Assume (Formula presented.). If K is sufficiently homogeneous, then we can say much more. For example, we prove that (Formula presented.) for a generic (Formula presented.) for all (Formula presented.) if and only if (Formula presented.) or (Formula presented.) for all open sets (Formula presented.). This is new even if (Formula presented.) and (Formula presented.). It is known that for a generic (Formula presented.) the interior of f(K) is not empty. We augment the above characterization by showing that (Formula presented.) for a generic (Formula presented.). In particular, almost every point of f(K) is an interior point. In order to obtain more precise results, we use the concept of generalized Hausdorff and packing measures, too. © 2017 Springer-Verlag Wien},
	keywords = {FIBERS; Hausdorff dimension; continuous functions; LEVEL SETS; Topological dimension; packing dimension; generic; Typical},
	year = {2017},
	eissn = {1436-5081},
	pages = {339-378}
}

@article{MTMT:3122467,
	title = {Increasing subsequences of random walks},
	url = {https://m2.mtmt.hu/api/publication/3122467},
	author = {ANGEL, O and Balka, Richárd and PERES, Y},
	doi = {10.1017/S0305004116000797},
	journal-iso = {MATH PROC CAMBRIDGE},
	journal = {MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY},
	volume = {163},
	unique-id = {3122467},
	issn = {0305-0041},
	abstract = {Given a sequence of n real numbers {Si }i⩽n, we consider the longest weakly increasing subsequence, namely i 1 < i 2 < . . . < iL with Sik ⩽ Sik+1 and L maximal. When the elements Si are i.i.d. uniform random variables, Vershik and Kerov, and Logan and Shepp proved that (Formula presented.). We consider the case when {Si }i⩽n is a random walk on ℝ with increments of mean zero and finite (positive) variance. In this case, it is well known (e.g., using record times) that the length of the longest increasing subsequence satisfies (Formula presented.). Our main result is an upper bound (Formula presented.), establishing the leading asymptotic behavior. If {Si }i⩽n is a simple random walk on ℤ, we improve the lower bound by showing that (Formula presented.). We also show that if { S i } is a simple random walk in ℤ2, then there is a subsequence of { S i }i⩽n of expected length at least cn 1/3 that is increasing in each coordinate. The above one-dimensional result yields an upper bound of n 1/2+o(1). The problem of determining the correct exponent remains open. Copyright © Cambridge Philosophical Society 2016},
	year = {2017},
	eissn = {1469-8064},
	pages = {173-185}
}

@article{MTMT:3064913,
	title = {Bruckner–Garg-Type Results with Respect to Haar Null Sets in C[0,1]},
	url = {https://m2.mtmt.hu/api/publication/3064913},
	author = {Balka, Richárd and Darji, U B and Elekes, Márton},
	doi = {10.1017/S0013091515000577},
	journal-iso = {P EDINBURGH MATH SOC},
	journal = {PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY},
	volume = {60},
	unique-id = {3064913},
	issn = {0013-0915},
	keywords = {MAPS; PREVALENT; continuous functions; continuous functions; LEVEL SETS; Haar null; Shy; Haar ambivalent},
	year = {2017},
	eissn = {1464-3839},
	pages = {17-30},
	orcid-numbers = {Elekes, Márton/0000-0002-5139-2169}
}