arXiv subjects

Yu Kitagawa

Publications and source records attributed to Yu Kitagawa.

3 recordsLinked to original sources

arXiv2026

Integrability of Freely Infinitely Divisible Distributions and L\'evy Measures

Under a growth condition on an increasing function $g$, we prove that integrability of a freely infinitely divisible distribution with respect to $g$ is equivalent to that of the large-jump part of its free L\'evy measure. For every increasing freely submultiplicative function $g$, integrability of the distribution implies integrability of the large-jump part of its free L\'evy measure. We also obtain two-sided tail comparisons between freely infinitely divisible distributions and their free L\'evy measures, uniform integrability along free convolution semigroups, and integrability results and tail estimates for fractional free convolution powers.

math.PR↗

arXiv2026

Freely infinitely divisible $R$-diagonal elements and Brown measure

We study freely infinitely divisible $R$-diagonal elements in the unbounded setting and Brown measures for free additive perturbations by such elements. This class includes circular elements, circular Cauchy elements, and other previously studied $R$-diagonal models. We construct examples and prove stability under several algebraic operations, including homogeneous noncommutative polynomials in bounded, freely independent elements from this class. Using results for general $R$-diagonal perturbations, together with several analytic estimates specific to freely infinitely divisible $R$-diagonal elements, we prove that, in the bounded case, the support of the Brown measure coincides with the spectrum, and we obtain a criterion for property (H) in this non-normal setting. Finally, we study the free convolution semigroup associated with the symmetrized law of the modulus and derive a Hamilton--Jacobi equation for the regularized logarithmic potential.

math.OA↗

arXiv2025

Free multiplicative convolution with an arbitrary measure on the real line

We develop analytic tools for studying the free multiplicative convolution of any measure on the real line and any measure on the nonnegative real line. More precisely, we construct the subordination functions and the $S$-transform of an arbitrary probability measure. The important multiplicativity of $S$-transform is proved with the help of subordination functions. We then apply the $S$-transform to establish convolution identities for stable laws, which had been considered in the literature only for the positive and symmetric cases. Subordination functions are also used in order to extend Belinschi--Nica's semigroup of homomorphisms, and to establish regularity properties of free multiplicative convolution, in particular, the absence of singular continuous part and analyticity of the density.

math.PR↗