Asymptotic Semicircular Law Induced by p-Adic Number Fields $$\mathbb {Q}_{p}$$ Q p Over Primes

Abstract

In this paper, we study asymptotic semicircular law, and corresponding free-distributional data, induced by p-adic analysis on the p-adic number fields $$\mathbb {Q}_{p}$$ , as $$p \rightarrow \infty $$ in the set $$ \mathcal {P}$$ of all primes.