Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 5

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last

Wyniki wyszukiwania

help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available remote

The arithmetic of distributions in free probability theory

100%
Chistyakov G., Götze F.
Open Mathematics
|
2011
|
tom 9
|
nr 5
997-1050
EN
We give an analytical approach to the definition of additive and multiplicative free convolutions which is based on the theory of Nevanlinna and Schur functions. We consider the set of probability distributions as a semigroup M equipped with the operation of free convolution and prove a Khintchine type theorem for the factorization of elements of this semigroup. An element of M contains either indecomposable (“prime”) factors or it belongs to a class, say I 0, of distributions without indecomposable factors. In contrast to the classical convolution semigroup, in the free additive and multiplicative convolution semigroups the class I 0 consists of units (i.e. Dirac measures) only. Furthermore we show that the set of indecomposable elements is dense in M.
2
Content available remote

Limit theorems in free probability theory II

100%
Chistyakov G., Götze F.
Open Mathematics
|
2008
|
tom 6
|
nr 1
87-117
EN
Based on an analytical approach to the definition of multiplicative free convolution on probability measures on the nonnegative line ℝ+ and on the unit circle $$ \mathbb{T} $$ we prove analogs of limit theorems for nonidentically distributed random variables in classical Probability Theory.
3
Content available remote

The rate of convergence for spectra of GUE and LUE matrix ensembles

100%
Götze F., Tikhomirov A.
Open Mathematics
|
2005
|
tom 3
|
nr 4
666-704
EN
We obtain optimal bounds of order O(n −1) for the rate of convergence to the semicircle law and to the Marchenko-Pastur law for the expected spectral distribution functions of random matrices from the GUE and LUE, respectively.
4
Content available remote

Rate of convergence to the semi-circle law for the Deformed Gaussian Unitary Ensemble

81%
Götze F., Tikhomirov A., Timushev D.
Open Mathematics
|
2007
|
tom 5
|
nr 2
305-334
EN
It is shown that the Kolmogorov distance between the expected spectral distribution function of an n × n matrix from the Deformed Gaussian Ensemble and the distribution function of the semi-circle law is of order O(n −2/3+v ).
5
Content available remote

Lower bounds for the number of integral polynomials with given order of discriminants

81%
Bernik V., Götze F., Kukso O.
Acta Arithmetica
|
2008
|
tom 133
|
nr 4
375-390
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.