Related papers: Classical and free infinite divisibility for Boole…
Consider a sequence of polynomials of bounded degree evaluated in independent Gaussian, Gamma or Beta random variables. We show that, if this sequence converges in law to a nonconstant distribution, then (i) the limit distribution is…
This paper proposes an algorithm for deciding consistency of systems of Boolean equations in several variables with co-efficients in the two element Boolean algebra $B_{0}=\{0,1\}$ and find all satisfying assignments. The algorithm is based…
We investigate analytical properties of free stable distributions and discover many connections with their classical counterparts. Our main result is an explicit formula for the Mellin transform, which leads to explicit series…
In this paper, by establishing a Borel-Cantelli lemma for a capacity which is not necessarily continuous, and a link between a sequence of independent random variables under the sub-linear expectation and a sequence of independent random…
Bercovici and Pata showed that the correspondence between classically, freely, and Boolean infinitely divisible distributions holds on the level of limit theorems. We extend this correspondence also to distributions infinitely divisible…
We prove that the classical normal distribution is infinitely divisible with respect to the free additive convolution. We study the Voiculescu transform first by giving a survey of its combinatorial implications and then analytically,…
We prove that symmetric Meixner distributions, whose probability densities are proportional to $|\Gamma(t+ix)|^2$, are freely infinitely divisible for $0<t\leq\frac{1}{2}$. The case $t=\frac{1}{2}$ corresponds to the law of L\'evy's…
In this thesis we study convolutions that arise from noncommutative probability theory. We prove several regularity results for free convolutions, and for measures in partially defined one-parameter free convolution semigroups. We discuss…
We give a complete list of the Lebesgue-Jordan decomposition of Boolean and monotone stable distributions and a complete list of the mode of them. They are not always unimodal.
We investigate the finite-time stabilization of a tree-shaped network of strings. Transparent boundary conditions are applied at all the external nodes. At any internal node, in addition to the usual continuity conditions, a modified…
Belinschi et al. [Adv. Math., 226 (2011), 3677--3698] proved that the normal distribution is freely infinitely divisible. This paper establishes a certain monotonicity, real analyticity and asymptotic behavior of the density of the free…
The phenomenon of superconvergence is proved for all freely infinitely divisible distributions. Precisely, suppose that the partial sums of a sequence of free identically distributed, infinitesimal random variables converge in distribution…
The well known Boole-Shannon expansion of Boolean functions in several variables (with co-efficients in a Boolean algebra $B$) is also known in more general form in terms of expansion in a set $\Phi$ of orthonormal functions. However,…
It is known that real Non-Gaussian stable distributions are unimodal, not additive strongly unimodal, and multiplicative strongly unimodal in the symmetric case. By a theorem of Cuculescu-Theodorescu, the only remaining relevant situation…
We prove that the distribution of the product of two correlated normal random variables with arbitrary means and arbitrary variances is infinitely divisible. We also obtain exact formulas for the probability density function of the sum of…
For each positive number $\alpha$ we study the analog $\nu_alpha$ in free probability of the classical Gamma distribution with parameter $\alpha$. We prove that $\nu_\alpha$ is absolutely continuous and establish the main properties of the…
A new class of fully decoupled consistent splitting schemes for the Navier-Stokes equations are constructed and analyzed in this paper. The schemes are based on the Taylor expansion at $t^{n+\beta}$ with $\beta\ge 1$ being a free parameter.…
We study the max-convolution and max-stable laws for Boolean independence and prove that these are Dagum distributions (also known as log-logistical distributions).
This paper proves long-standing conjectures regarding the existence of infinitely many high-frequency modulational instability ``isolas" for a Stokes wave in arbitrary depth $ \mathtt{h} > 0 $, under longitudinal perturbations. We provide a…
We consider classes of Boolean functions stable under compositions both from the right and from the left with clones. Motivated by the question how many properties of Boolean functions can be defined by means of linear equations, we focus…