@article{MTMT:33693733,
	title = {Positive Polynomials and Boundary Interpolation with Finite Blaschke Products},
	url = {https://m2.mtmt.hu/api/publication/33693733},
	author = {Kalmykov, Sergei and Nagy, Béla},
	doi = {10.1007/s40315-021-00430-4},
	journal-iso = {COMPUT METH FUNCT TH},
	journal = {COMPUTATIONAL METHODS AND FUNCTION THEORY},
	volume = {23},
	unique-id = {33693733},
	issn = {1617-9447},
	abstract = {The famous Jones–Ruscheweyh theorem states that n distinct points on the unit circle can be mapped to n arbitrary points on the unit circle by a Blaschke product of degree at most n-1 n - 1 . In this paper, we provide a new proof using real algebraic techniques. First, the interpolation conditions are rewritten into complex equations. These complex equations are transformed into a system of polynomial equations with real coefficients. This step leads to a “geometric representation” of Blaschke products. Then another set of transformations is applied to reveal some structure of the equations. Finally, the following two fundamental tools are used: a Positivstellensatz by Prestel and Delzell describing positive polynomials on compact semialgebraic sets using Archimedean module of length N . The other tool is a representation of positive polynomials in a specific form due to Berr and Wörmann. This, combined with a careful calculation of leading terms of occurring polynomials finishes the proof.},
	year = {2023},
	eissn = {2195-3724},
	pages = {49-72},
	orcid-numbers = {Nagy, Béla/0000-0002-8323-4050}
}

@article{MTMT:33578758,
	title = {Isometric rigidity of Wasserstein tori and spheres},
	url = {https://m2.mtmt.hu/api/publication/33578758},
	author = {Gehér, György and Titkos, Tamás and Virosztek, Dániel},
	doi = {10.1112/mtk.12174},
	journal-iso = {MATHEMATIKA},
	journal = {MATHEMATIKA},
	volume = {69},
	unique-id = {33578758},
	issn = {0025-5793},
	abstract = {We prove isometric rigidity for p-Wasserstein spaces over finite-dimensional tori and spheres for all p. We present a unified approach to proving rigidity that relies on the robust method of recovering measures from their Wasserstein potentials. © 2022 The Authors. The publishing rights in this article are licensed to University College London under an exclusive licence. Mathematika is published by the London Mathematical Society on behalf of University College London.},
	year = {2023},
	eissn = {2041-7942},
	pages = {20-32},
	orcid-numbers = {Gehér, György/0000-0003-1499-3229}
}

@article{MTMT:33578756,
	title = {Quantum Wasserstein isometries on the qubit state space},
	url = {https://m2.mtmt.hu/api/publication/33578756},
	author = {Gehér, György and Pitrik, József and Titkos, Tamás and Virosztek, Dániel},
	doi = {10.1016/j.jmaa.2022.126955},
	journal-iso = {J MATH ANAL APPL},
	journal = {JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS},
	volume = {522},
	unique-id = {33578756},
	issn = {0022-247X},
	abstract = {We describe Wasserstein isometries of the quantum bit state space with respect to distinguished cost operators. We derive a Wigner-type result for the cost operator involving all the Pauli matrices: in this case, the isometry group consists of unitary or anti-unitary conjugations. In the Bloch sphere model this means that the isometry group coincides with the classical symmetry group O(3). On the other hand, for the cost generated by the qubit ‘‘clock” and ‘‘shift” operators, we discovered non-surjective and non-injective isometries as well, beyond the regular ones. This phenomenon mirrors certain surprising properties of the quantum Wasserstein distance. © 2022 Elsevier Inc.},
	keywords = {isometries; Quantum bits; Quantum optimal transport},
	year = {2023},
	eissn = {1096-0813},
	orcid-numbers = {Gehér, György/0000-0003-1499-3229}
}

@article{MTMT:33343742,
	title = {Reflections on a theorem of V. Andrievskii},
	url = {https://m2.mtmt.hu/api/publication/33343742},
	author = {Totik, Vilmos},
	doi = {10.1007/s11854-022-0241-4},
	journal-iso = {J ANAL MATH},
	journal = {JOURNAL D ANALYSE MATHEMATIQUE},
	volume = {148},
	unique-id = {33343742},
	issn = {0021-7670},
	abstract = {For a given point of a compact subset E of the real line four properties are proven to be pairwise equivalent: local Bernstein-inequality, local higher-order Bernstein-inequality, local Lip 1 continuity of the Green's function and local Lip 1 property of the equilibrium measure. Furthermore, in connection with a result of V. Andrievkskii, it is shown that these equivalent properties are closely related to Bernstein's approximation theorem and its generalization given by R. K. Vasiliev. Similar results are established at endpoints of subintervals of E, where the local Bernstein-inequality is replaced by the local Markov-inequality and Lip 1 is replaced by Lip 1/2.},
	year = {2022},
	eissn = {1565-8538},
	pages = {711-738}
}

@article{MTMT:32860302,
	title = {Convergence of partial sum processes to stable processes with application for aggregation of branching processes},
	url = {https://m2.mtmt.hu/api/publication/32860302},
	author = {Barczy, Mátyás and Nedényi, Fanni and Pap, Gyula},
	doi = {10.1214/21-BJPS528},
	journal-iso = {BRAZ J PROBAB STAT},
	journal = {BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS},
	volume = {36},
	unique-id = {32860302},
	issn = {0103-0752},
	year = {2022},
	eissn = {0103-0752},
	pages = {315-348},
	orcid-numbers = {Barczy, Mátyás/0000-0003-3119-7953; Nedényi, Fanni/0000-0001-8552-0168}
}

@article{MTMT:32518308,
	title = {Random Means Generated by Random Variables: Expectation and Limit Theorems},
	url = {https://m2.mtmt.hu/api/publication/32518308},
	author = {Barczy, Mátyás and Burai, Pál József},
	doi = {10.1007/s00025-021-01541-z},
	journal-iso = {RES MATHEM},
	journal = {RESULTS IN MATHEMATICS},
	volume = {77},
	unique-id = {32518308},
	issn = {1422-6383},
	year = {2022},
	eissn = {1420-9012},
	orcid-numbers = {Barczy, Mátyás/0000-0003-3119-7953}
}

@article{MTMT:32273473,
	title = {Limit theorems for Bajraktarevic and Cauchy quotient means of independent identically distributed random variables},
	url = {https://m2.mtmt.hu/api/publication/32273473},
	author = {Barczy, Mátyás and Burai, Pál József},
	doi = {10.1007/s00010-021-00813-x},
	journal-iso = {AEQUATIONES MATH},
	journal = {AEQUATIONES MATHEMATICAE},
	volume = {96},
	unique-id = {32273473},
	issn = {0001-9054},
	abstract = {We derive strong laws of large numbers and central limit theorems for Bajraktarevic, Gini and exponential- (also called Beta-type) and logarithmic Cauchy quotient means of independent identically distributed (i.i.d.) random variables. The exponential- and logarithmic Cauchy quotient means of a sequence of i.i.d. random variables behave asymptotically normal with the usual square root scaling just like the geometric means of the given random variables. Somewhat surprisingly, the multiplicative Cauchy quotient means of i.i.d. random variables behave asymptotically in a rather different way: in order to get a non-trivial normal limit distribution a time dependent centering is needed.},
	keywords = {central limit theorem; Delta method; Bajraktarević mean; Gini mean; Cauchy quotient means; Beta-type mean},
	year = {2022},
	eissn = {1420-8903},
	pages = {279-305},
	orcid-numbers = {Barczy, Mátyás/0000-0003-3119-7953}
}

@article{MTMT:31507577,
	title = {A new example for a proper scoring rule},
	url = {https://m2.mtmt.hu/api/publication/31507577},
	author = {Barczy, Mátyás},
	doi = {10.1080/03610926.2020.1801737},
	journal-iso = {COMMUN STAT-THEOR M},
	journal = {COMMUNICATIONS IN STATISTICS-THEORY AND METHODS},
	volume = {55},
	unique-id = {31507577},
	issn = {0361-0926},
	abstract = {We give a new example for a proper scoring rule motivated by the form of Anderson-Darling distance of distribution functions and an example of Brehmer and Gneiting.},
	keywords = {Scoring rule; properization; weighted Continuous Ranked Probability Scoring rule},
	year = {2022},
	eissn = {1532-415X},
	pages = {3705-3712},
	orcid-numbers = {Barczy, Mátyás/0000-0003-3119-7953}
}

@article{MTMT:32708441,
	title = {The Beckman–Quarles theorem via the triangle inequality},
	url = {https://m2.mtmt.hu/api/publication/32708441},
	author = {Totik, Vilmos},
	doi = {10.1515/advgeom-2020-0024},
	journal-iso = {ADV GEOM},
	journal = {ADVANCES IN GEOMETRY},
	volume = {21},
	unique-id = {32708441},
	issn = {1615-715X},
	year = {2021},
	eissn = {1615-7168},
	pages = {541-543}
}

@article{MTMT:32705167,
	title = {A note on asymptotic behavior of critical Galton–Watson processes with immigration},
	url = {https://m2.mtmt.hu/api/publication/32705167},
	author = {Barczy, Mátyás and Bezdány, Dániel and Pap, Gyula},
	doi = {10.2140/involve.2021.14.871},
	journal-iso = {INVOLVE: J MATH},
	journal = {INVOLVE: A JOURNAL OF MATHEMATICS},
	volume = {14},
	unique-id = {32705167},
	issn = {1944-4176},
	abstract = {In this somewhat didactic note we give a detailed alternative proof of the known result of Wei and Winnicki (1989) which states that, under second-order moment assumptions on the offspring and immigration distributions, the sequence of appropriately scaled random step functions formed from a critical Galton–Watson process with immigration (not necessarily starting from zero) converges weakly towards a squared Bessel process. The proof of Wei and Winnicki (1989) is based on infinitesimal generators, while we use limit theorems for random step processes towards a diffusion process due to Ispány and Pap (2010). This technique was already used by Ispány (2008), who proved functional limit theorems for a sequence of some appropriately normalized nearly critical Galton–Watson processes with immigration starting from zero, where the offspring means tend to its critical value 1. As a special case of Theorem 2.1 of Ispány (2008) one can get back the result of Wei and Winnicki (1989) in the case of zero initial value. In the present note we handle nonzero initial values with the technique used by Ispány (2008), and further, we simplify some of the arguments in the proof of Theorem 2.1 of Ispány (2008) as well.},
	year = {2021},
	eissn = {1944-4184},
	pages = {871-891},
	orcid-numbers = {Barczy, Mátyás/0000-0003-3119-7953}
}