Deformation of semicircular and circular laws via p-adic number fields and sampling of primes

• Autorzy: Cho Ilwoo , Jorgensen Palie E. T.

Identyfikatory

DOI

10.7494/OpMath.2019.39.6.773

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

free probability; primes; p-adic number fields; Banach *-probability spaces semicircular elements; circular elements; truncated linear functionals

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2019
• Tom: Vol. 39, no. 6
• Strony: 773--813
• Opis fizyczny: Bibliogr. 29 poz.

Twórcy

autor

Cho Ilwoo

• Saint Ambrose University Department of Mathematics and Statistics 421 Ambrose Hall, 518 W. Locust St. Davenport, Iowa, 52803, USA

autor

Jorgensen Palie E. T.

• The University of Iowa Department of Mathematics Iowa City, IA 52242-1419, USA

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