@article{MTMT:34767259,
	title = {Geometric relative entropies and barycentric Rényi divergences},
	url = {https://m2.mtmt.hu/api/publication/34767259},
	author = {Mosonyi, Milán and Bunth, Gergely and Vrana, Péter},
	journal-iso = {LINEAR ALGEBRA APPL},
	journal = {LINEAR ALGEBRA AND ITS APPLICATIONS},
	volume = {accepted: 15 Oct 2023},
	unique-id = {34767259},
	issn = {0024-3795},
	abstract = {We give systematic ways of defining monotone quantum relative entropies and (multi-variate) quantum Rényi divergences starting from a set of monotone quantum relative entropies.
		Despite its central importance in information theory, only two additive and monotone quantum extensions of the classical relative entropy have been known so far, the Umegaki and the Belavkin-Staszewski relative entropies. Here we give a general procedure to construct monotone and additive quantum relative entropies from a given one with the same properties; in particular, when starting from the Umegaki relative entropy, this gives a new one-parameter family of monotone and additive quantum relative entropies interpolating between the Umegaki and the Belavkin-Staszewski ones on full-rank states.
		In a different direction, we use a generalization of a classical variational formula to define multi-variate quantum Rényi quantities corresponding to any finite set of quantum relative entropies (Dqx)x∈X and signed probability measure P, as
		Qb,qP((ρx)x∈X):=supτ≥0{Trτ−∑xP(x)Dqx(τ∥ρx)}.
		We show that monotone quantum relative entropies define monotone Rényi quantities whenever P is a probability measure. With the proper normalization, the negative logarithm of the above quantity gives a quantum extension of the classical Rényi α-divergence in the 2-variable case (X={0,1}, P(0)=α). We show that if both Dq0 and Dq1 are monotone and additive quantum relative entropies, and at least one of them is strictly larger than the Umegaki relative entropy then the resulting barycentric Rényi divergences are strictly between the log-Euclidean and the maximal Rényi divergences, and hence they are different from any previously studied quantum Rényi divergence.},
	year = {2024},
	eissn = {1873-1856},
	pages = {&},
	orcid-numbers = {Mosonyi, Milán/0000-0002-5973-5533; Vrana, Péter/0000-0003-0770-0432}
}

@article{MTMT:34554367,
	title = {On some algebraic properties related to Heron type operator means on positive definite cones of C⁎-algebras},
	url = {https://m2.mtmt.hu/api/publication/34554367},
	author = {Molnár, Lajos and Simon, Richárd},
	doi = {10.1016/j.laa.2023.12.023},
	journal-iso = {LINEAR ALGEBRA APPL},
	journal = {LINEAR ALGEBRA AND ITS APPLICATIONS},
	volume = {685},
	unique-id = {34554367},
	issn = {0024-3795},
	abstract = {In this paper we consider certain algebraic properties concerning variants of the Heron mean on positive definite cones of general C⁎-algebras. Those variants are the Kubo-Ando type Heron mean and the Wasserstein mean. The main part of the investigation concerns associativity properties. We present a number of results that show how far operations related to those two kinds of means are from being associative. Many of our results can also be viewed as characterizations of central positive definite elements or as characterizations of commutative C⁎-algebras. © 2023 Elsevier Inc.},
	keywords = {Associativity; Algebra; Kubo-Ando means; C*-algebra; C*-algebra; Positive definite cone; Positive definite cone; Kubo–Ando mean; Positive definite; Heron mean; Heron mean; Wasserstein mean; Wasserstein mean; Bisymmetry; Associativity related equalities; Associativity related equality; Bisymmetry equation; Bisymmetry equation},
	year = {2024},
	eissn = {1873-1856},
	pages = {214-246}
}

@article{MTMT:34429446,
	title = {Tiling and weak tiling in (Zp)d},
	url = {https://m2.mtmt.hu/api/publication/34429446},
	author = {Kiss, Gergely and Matolcsi, Dávid and Matolcsi, Máté and Somlai, Gábor},
	doi = {10.1007/s43670-023-00073-7},
	journal-iso = {Sampl. Theory Signal Process. Data Anal.},
	journal = {Sampling Theory, Signal Processing, and Data Analysis},
	volume = {22},
	unique-id = {34429446},
	issn = {2730-5716},
	abstract = {We discuss the relation of tiling, weak tiling and spectral sets in finite abelian groups. In particular, in elementary p -groups (\mathbb {Z}_p)^d ( Z p ) d , we introduce an averaging procedure that leads to a natural object of study: a 4-tuple of functions which can be regarded as a common generalization of tiles and spectral sets. We characterize such 4-tuples for d=1, 2 d = 1 , 2 , and prove some partial results for d=3 d = 3 .},
	year = {2024},
	eissn = {2730-5724},
	orcid-numbers = {Matolcsi, Máté/0000-0003-4889-697X; Somlai, Gábor/0000-0001-5761-7579}
}

@article{MTMT:34231287,
	title = {Some continuity properties of quantum Rényi divergences},
	url = {https://m2.mtmt.hu/api/publication/34231287},
	author = {Mosonyi, Milán and Hiai, F.},
	doi = {10.1109/TIT.2023.3324758},
	journal-iso = {IEEE T INFORM THEORY},
	journal = {IEEE TRANSACTIONS ON INFORMATION THEORY},
	volume = {70},
	unique-id = {34231287},
	issn = {0018-9448},
	year = {2024},
	eissn = {1557-9654},
	pages = {2674-2700},
	orcid-numbers = {Mosonyi, Milán/0000-0002-5973-5533}
}

@article{MTMT:34118222,
	title = {p-Capacity with Bessel Convolution},
	url = {https://m2.mtmt.hu/api/publication/34118222},
	author = {G. Horváth, Ágota},
	doi = {10.1007/s11118-023-10097-2},
	journal-iso = {POTENTIAL ANAL},
	journal = {POTENTIAL ANALYSIS},
	volume = {60},
	unique-id = {34118222},
	issn = {0926-2601},
	abstract = {We define and examine nonlinear potential by Bessel convolution with Bessel kernel. We investigate removable sets with respect to Laplace-Bessel inequality. By studying the maximal and fractional maximal measure, a Wolff type inequality is proved. Finally the relation of B- p capacity and B-Lipschitz mapping, and the B- p capacity and weighted Hausdorff measure and the B- p capacity of Cantor sets are examined.},
	year = {2024},
	eissn = {1572-929X},
	pages = {1487-1511},
	orcid-numbers = {G. Horváth, Ágota/0000-0002-5836-7548}
}

@article{MTMT:33834838,
	title = {The density of planar sets avoiding unit distances},
	url = {https://m2.mtmt.hu/api/publication/33834838},
	author = {Ambrus, Gergely and Csiszárik, Adrián and Matolcsi, Máté and Varga, Dániel and Zsámboki, Pál},
	doi = {10.1007/s10107-023-02012-9},
	journal-iso = {MATH PROGRAM},
	journal = {MATHEMATICAL PROGRAMMING},
	volume = {Published: 06 October 2023},
	unique-id = {33834838},
	issn = {0025-5610},
	abstract = {By improving upon previous estimates on a problem posed by L. Moser, we prove a conjecture of Erdős that the density of any measurable planar set avoiding unit distances is less than 1/4. Our argument implies the upper bound of 0.2470.},
	year = {2024},
	eissn = {1436-4646},
	orcid-numbers = {Ambrus, Gergely/0000-0003-1246-6601; Matolcsi, Máté/0000-0003-4889-697X}
}

@article{MTMT:33742874,
	title = {On a parametric family of distance measures that includes the Hellinger and the Bures distances},
	url = {https://m2.mtmt.hu/api/publication/33742874},
	author = {Komálovics, A. and Molnár, Lajos},
	doi = {10.1016/j.jmaa.2023.127226},
	journal-iso = {J MATH ANAL APPL},
	journal = {JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS},
	volume = {529},
	unique-id = {33742874},
	issn = {0022-247X},
	abstract = {In this paper we define a parametric family of certain two-variable maps on positive cones of C*-algebras. The square roots of the values of those maps under a faithful tracial positive linear functional (in the cases where the square roots are well defined, i.e., those values are non-negative real numbers on the whole cones) as two-variable numerical functions can be considered as a family of potential distance measures which includes the well known Hellinger and Bures metrics. We study that family from various points of view. The main questions concern the mentioned problem of well-definedness and, whenever we have an affirmative answer to that question, the problem whether those distance measures are true metrics. Besides, we obtain some related trace characterizations. Our study is not complete, we formulate a few probably quite difficult open questions.(c) 2023 Elsevier Inc. All rights reserved.},
	keywords = {DETERMINANT; SPACES; inequality; Distance measure; C*-algebra; C-ASTERISK-ALGEBRAS; Positive cone; Mathematics, Applied; Hellinger and Bures metrics; Tracial linear functional},
	year = {2024},
	eissn = {1096-0813}
}

@article{MTMT:33669185,
	title = {Ergodic aspects of trading with threshold strategies},
	url = {https://m2.mtmt.hu/api/publication/33669185},
	author = {Lovas, Attila and Rásonyi, Miklós},
	doi = {10.1007/s10479-023-05233-5},
	journal-iso = {ANN OPER RES},
	journal = {ANNALS OF OPERATIONS RESEARCH},
	volume = {Published: 22 February 2023},
	unique-id = {33669185},
	issn = {0254-5330},
	abstract = {To profit from price oscillations, investors frequently use threshold-type strategies where changes in the portfolio position are triggered by some indicators reaching prescribed levels. In this paper we investigate threshold-type strategies in the context of ergodic control. We make the first steps towards their optimization by proving ergodic properties of related functionals. Assuming Markovian price increments satisfying a minorization condition and (one-sided) boundedness we show, in particular, that for given thresholds, the distribution of the gains converges in the long run. We also extend recent results on the stability of overshoots of random walks from the i.i.d. increment case to Markovian increments, under suitable conditions.},
	year = {2024},
	eissn = {1572-9338}
}

@{MTMT:34470967,
	title = {Applications of the Automatic Additivity of Positive Homogeneous Order Isomorphisms Between Positive Definite Cones in C∗ -Algebras},
	url = {https://m2.mtmt.hu/api/publication/34470967},
	author = {Molnár, Lajos},
	booktitle = {Function Spaces, Theory and Applications},
	doi = {10.1007/978-3-031-39270-2_4},
	volume = {87},
	unique-id = {34470967},
	keywords = {symmetries; preservers; isometries; isomorphisms; Operator means; positive cones; C∗ -Algebras},
	year = {2023},
	pages = {77-104}
}

@article{MTMT:34217373,
	title = {Spectral sets and weak tiling},
	url = {https://m2.mtmt.hu/api/publication/34217373},
	author = {Kolountzakis, M.N. and Lev, N. and Matolcsi, Máté},
	doi = {10.1007/s43670-023-00070-w},
	journal-iso = {Sampl. Theory Signal Process. Data Anal.},
	journal = {Sampling Theory, Signal Processing, and Data Analysis},
	volume = {21},
	unique-id = {34217373},
	issn = {2730-5716},
	year = {2023},
	eissn = {2730-5724},
	orcid-numbers = {Matolcsi, Máté/0000-0003-4889-697X}
}