A phase transition for tails of the free multiplicative convolution powers

Limits for Convolution Tails 3

Suppose F is a distribution on the half-line [0, ∞). We study the limits of the ratios of tails F * F (x)/F (x) as x → ∞. We also discuss the classes of distributions S , S (γ), and S * .

Spectral density of generalized Wishart matrices and free multiplicative convolution.

We investigate the level density for several ensembles of positive random matrices of a Wishart-like structure, W=XX(†), where X stands for a non-Hermitian random matrix. In particular, making use of the Cauchy transform, we study the free multiplicative powers of the Marchenko-Pastur (MP) distribution, MP(⊠s), which for an integer s yield Fuss-Catalan distributions corresponding to a product o...

The convolution inequality for entropy powers

investigating the feasibility of a proposed model for geometric design of deployable arch structures

deployable scissor type structures are composed of the so-called scissor-like elements (sles), which are connected to each other at an intermediate point through a pivotal connection and allow them to be folded into a compact bundle for storage or transport. several sles are connected to each other in order to form units with regular polygonal plan views. the sides and radii of the polygons are...

Probability MULTIPLICATIVE FREE CONVOLUTION AND INFORMATION - PLUS - NOISE TYPE MATRICES

Free probability and random matrix theory has shown to be a fruitful combination in many fields of research, such as digital communications, nuclear physics and mathematical finance. The link between free probability and eigenvalue distributions of random matrices will be strengthened further in this paper. It will be shown how the concept of multiplicative free convolution can be used to expre...