We examine the distributions of non-commutative polynomials of non-atomic, freely independent random variables. In particular, we obtain an analogue of the Strong Atiyah Conjecture for free groups, ...

In this study, we establish the Marcinkiewicz–Zygmund strong law of large numbers for randomly weighted sums of negatively orthant dependent random variables. The law of the single law of logarithm ...

Random analytic functions are a fundamental object of study in modern complex analysis and probability theory. These functions, often defined through power series with random coefficients, exhibit ...