scholarly journals Certain $*$-homomorphisms acting on unital $C^{*}$-probability spaces and semicircular elements induced by $p$-adic number fields over primes $p$

2020 ◽  
Vol 28 (2) ◽  
pp. 739-776
Author(s):  
Ilwoo Cho ◽  
Keyword(s):  
Number Fields ◽  
Probability Spaces ◽  
Semicircular Elements

scholarly journals Primes in Intervals and Semicircular Elements Induced by p-Adic Number Fields Qp over Primes p

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 199 ◽  
Author(s):  
Ilwoo Cho ◽  
Palle Jorgensen
Keyword(s):  
Probability Space ◽  
Free Probability ◽  
Number Fields ◽  
Linear Functionals ◽  
Real Numbers ◽  
Probabilistic Information ◽  
Closed Intervals ◽  
Measurable Functions ◽  
Semicircular Elements

In this paper, we study free probability on (weighted-)semicircular elements in a certain Banach *-probability space ( LS , τ 0 ) induced by measurable functions on p-adic number fields Q p over primes p . In particular, we are interested in the cases where such free-probabilistic information is affected by primes in given closed intervals of the set R of real numbers by defining suitable “truncated” linear functionals on LS .

scholarly journals Asymptotic Semicircular Laws Induced by p-Adic Number Fields Qp and C-Algebras over Primes p*

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 819
Author(s):  
Ilwoo Cho
Keyword(s):  
Number Fields ◽  
C Algebras ◽  
Probability Spaces

In this paper, we study asymptotic semicircular laws induced both by arbitrarily fixed C * -probability spaces, and p-adic number fields { Q p } p ∈ P , as p→∞ in the set P of all primes.

scholarly journals Semicircular elements induced by p-adic number fields

2017 ◽  
Vol 37 (45) ◽  
pp. 665 ◽  
Author(s):  
Ilwoo Cho ◽  
Palle E. T. Jorgensen
Keyword(s):  
Number Fields ◽  
Semicircular Elements

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

2019 ◽  
Vol 39 (6) ◽  
pp. 773-813
Author(s):  
Ilwoo Cho ◽  
Palle E. T. Jorgensen
Keyword(s):  
Banach Algebra ◽  
Probability Space ◽  
Number Fields ◽  
Linear Functionals ◽  
Real Numbers ◽  
Circular Law ◽  
Semicircular Law ◽  
Different Types ◽  
Semicircular Elements

In this paper, we study semicircular elements and circular elements in a certain Banach \(*\)-probability space \((\mathfrak{LS},\tau ^{0})\) induced by analysis on the \(p\)-adic number fields \(\mathbb{Q}_{p}\) over primes \(p\). In particular, by truncating the set \(\mathcal{P}\) of all primes for given suitable real numbers \(t\lt s\) in \(\mathbb{R}\), two different types of truncated linear functionals \(\tau_{t_{1}\lt t_{2}}\), and \(\tau_{t_{1}\lt t_{2}}^{+}\) are constructed on the Banach \(*\)-algebra \(\mathfrak{LS}\). We show how original free distributional data (with respect to \(\tau ^{0}\)) are distorted by the truncations on \(\mathcal{P}\) (with respect to \(\tau_{t\lt s}\), and \(\tau_{t\lt s}^{+}\)). As application, distorted free distributions of the semicircular law, and those of the circular law are characterized up to truncation.

scholarly journals Banach-Space Operators Acting on Semicircular Elements Induced by p-Adic Number Fields over Primes p

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 498
Author(s):  
Ilwoo Cho
Keyword(s):  
Banach Space ◽  
Probability Space ◽  
Number Fields ◽  
Semicircular Elements ◽  
Banach Space Operators

In this paper, we study certain Banach-space operators acting on the Banach *-probability space ( LS , τ 0 ) generated by semicircular elements Θ p , j induced by p-adic number fields Q p over the set P of all primes p. Our main results characterize the operator-theoretic properties of such operators, and then study how ( LS , τ 0 ).

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