TY - JOUR AU - Kalmykov, Sergei AU - Nagy, Béla TI - Positive Polynomials and Boundary Interpolation with Finite Blaschke Products JF - COMPUTATIONAL METHODS AND FUNCTION THEORY J2 - COMPUT METH FUNCT TH VL - 23 PY - 2023 IS - 1 SP - 49 EP - 72 PG - 24 SN - 1617-9447 DO - 10.1007/s40315-021-00430-4 UR - https://m2.mtmt.hu/api/publication/33693733 ID - 33693733 AB - 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. LA - English DB - MTMT ER - TY - JOUR AU - Gehér, György AU - Titkos, Tamás AU - Virosztek, Dániel TI - Isometric rigidity of Wasserstein tori and spheres JF - MATHEMATIKA J2 - MATHEMATIKA VL - 69 PY - 2023 IS - 1 SP - 20 EP - 32 PG - 13 SN - 0025-5793 DO - 10.1112/mtk.12174 UR - https://m2.mtmt.hu/api/publication/33578758 ID - 33578758 N1 - Cited By :1 Export Date: 20 January 2023 Correspondence Address: Virosztek, D.; Alfréd Rényi Institute of Mathematics, Reáltanoda u. 13-15, Hungary; email: virosztek.daniel@renyi.hu Funding details: Leverhulme Trust, ECF‐2018‐125 Funding details: Magyar Tudományos Akadémia, MTA, K124152, KH129601, LP2021‐15/2021 Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFIH, K134944, PD128374 Funding text 1: Gehér was supported by the Leverhulme Trust Early Career Fellowship (ECF‐2018‐125), and also by the Hungarian National Research, Development and Innovation Office (Grant Number: K134944); Titkos was supported by the Hungarian National Research, Development and Innovation Office ‐ NKFIH (Grant Numbers: PD128374 and K134944) and by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences; Virosztek was supported by the Momentum program of the Hungarian Academy of Sciences under Grant Agreement Number: LP2021‐15/2021, and partially supported by the Hungarian National Research, Development and Innovation Office ‐ NKFIH (Grant Numbers: K124152 and KH129601). AB - 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. LA - English DB - MTMT ER - TY - JOUR AU - Gehér, György AU - Pitrik, József AU - Titkos, Tamás AU - Virosztek, Dániel TI - Quantum Wasserstein isometries on the qubit state space JF - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS J2 - J MATH ANAL APPL VL - 522 PY - 2023 IS - 2 PG - 17 SN - 0022-247X DO - 10.1016/j.jmaa.2022.126955 UR - https://m2.mtmt.hu/api/publication/33578756 ID - 33578756 N1 - Export Date: 08 March 2024 AB - 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. LA - English DB - MTMT ER - TY - JOUR AU - Totik, Vilmos TI - Reflections on a theorem of V. Andrievskii JF - JOURNAL D ANALYSE MATHEMATIQUE J2 - J ANAL MATH VL - 148 PY - 2022 SP - 711 EP - 738 PG - 28 SN - 0021-7670 DO - 10.1007/s11854-022-0241-4 UR - https://m2.mtmt.hu/api/publication/33343742 ID - 33343742 AB - 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. LA - English DB - MTMT ER - TY - JOUR AU - Barczy, Mátyás AU - Nedényi, Fanni AU - Pap, Gyula TI - Convergence of partial sum processes to stable processes with application for aggregation of branching processes JF - BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS J2 - BRAZ J PROBAB STAT VL - 36 PY - 2022 IS - 2 SP - 315 EP - 348 PG - 34 SN - 0103-0752 DO - 10.1214/21-BJPS528 UR - https://m2.mtmt.hu/api/publication/32860302 ID - 32860302 LA - English DB - MTMT ER - TY - JOUR AU - Barczy, Mátyás AU - Burai, Pál József TI - Random Means Generated by Random Variables: Expectation and Limit Theorems JF - RESULTS IN MATHEMATICS J2 - RES MATHEM VL - 77 PY - 2022 IS - 1 PG - 28 SN - 1422-6383 DO - 10.1007/s00025-021-01541-z UR - https://m2.mtmt.hu/api/publication/32518308 ID - 32518308 LA - English DB - MTMT ER - TY - JOUR AU - Barczy, Mátyás AU - Burai, Pál József TI - Limit theorems for Bajraktarevic and Cauchy quotient means of independent identically distributed random variables JF - AEQUATIONES MATHEMATICAE J2 - AEQUATIONES MATH VL - 96 PY - 2022 IS - 2 SP - 279 EP - 305 PG - 27 SN - 0001-9054 DO - 10.1007/s00010-021-00813-x UR - https://m2.mtmt.hu/api/publication/32273473 ID - 32273473 AB - 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. LA - English DB - MTMT ER - TY - JOUR AU - Barczy, Mátyás TI - A new example for a proper scoring rule JF - COMMUNICATIONS IN STATISTICS-THEORY AND METHODS J2 - COMMUN STAT-THEOR M VL - 55 PY - 2022 IS - 11 SP - 3705 EP - 3712 PG - 8 SN - 0361-0926 DO - 10.1080/03610926.2020.1801737 UR - https://m2.mtmt.hu/api/publication/31507577 ID - 31507577 AB - 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. LA - English DB - MTMT ER - TY - JOUR AU - Totik, Vilmos TI - The Beckman–Quarles theorem via the triangle inequality JF - ADVANCES IN GEOMETRY J2 - ADV GEOM VL - 21 PY - 2021 IS - 4 SP - 541 EP - 543 PG - 3 SN - 1615-715X DO - 10.1515/advgeom-2020-0024 UR - https://m2.mtmt.hu/api/publication/32708441 ID - 32708441 LA - English DB - MTMT ER - TY - JOUR AU - Barczy, Mátyás AU - Bezdány, Dániel AU - Pap, Gyula TI - A note on asymptotic behavior of critical Galton–Watson processes with immigration JF - INVOLVE: A JOURNAL OF MATHEMATICS J2 - INVOLVE: J MATH VL - 14 PY - 2021 IS - 5 SP - 871 EP - 891 PG - 21 SN - 1944-4176 DO - 10.2140/involve.2021.14.871 UR - https://m2.mtmt.hu/api/publication/32705167 ID - 32705167 AB - 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. LA - English DB - MTMT ER -