Autor: Jorgensen, Palie E. T. - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Deformation of semicircular and circular laws via p-adic number fields and sampling of primes
Autorzy:: Cho, Ilwoo
Jorgensen, Palie E. T.
Powiązania:: https://bibliotekanauki.pl/articles/255649.pdf
Data publikacji:: 2019
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: free probability
primes
p-adic number fields
Banach *-probability spaces semicircular elements
circular elements
truncated linear functionals
Opis:: In this paper, we study semicircular elements and circular elements in a certain Banach *-probability space [formula] induced by analysis on the p-adic number fields Qp over primes p. In particular, by truncating the set P of all primes for given suitable real numbers t < s in R, two different types of truncated linear functionals [formula], and [formula] re constructed on the Banach *-algebra [formula]. We show how original free distributional data (with respect to r°) are distorted by the truncations on P (with respect to [formula], and [formula]). As application, distorted free distributions of the semicircular law, and those of the circular law are characterized up to truncation.
Źródło:: Opuscula Mathematica; 2019, 39, 6; 773-813
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: Decomposition of Gaussian processes, and factorization of positive definite kernels
Autorzy:: Jorgensen, Palie E. T.
Tian, Feng
Powiązania:: https://bibliotekanauki.pl/articles/255819.pdf
Data publikacji:: 2019
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: reproducing kernel Hilbert space frames
generalized Ito-integration
the measurable category analysis/synthesis
interpolation
Gaussian free fields
non-uniform sampling
optimization
transform
covariance
feature space
Opis:: We establish a duality for two lactorization questions, one for general positive definite (p.d.) kernels K, and the other for Gaussian processes, say V. The latter notion, for Gaussian processes is stated via Ito-integration. Our approach to factorization for p.d. kernels is intuitively motivated by matrix factorizations, but in infinite dimensions, subtle measure theoretic issues must be addressed. Consider a given p.d. kernel K, presented as a covariance kernel for a Gaussian process V. We then give an explicit duality for these two seemingly different notions of factorization, for p.d. kernel K, vs for Gaussian process V. Our result is in the form of an explicit correspondence. It states that the analytic data which determine the variety of factorizations for K is the exact same as that which yield factorizations for V. Examples and applications are included: point-processes, sampling schemes, constructive discretization, graph-Laplacians, and boundary-value problems.
Źródło:: Opuscula Mathematica; 2019, 39, 4; 497-541
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

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