Results 41 to 50 of about 11,188 (189)
Notes on the Free Additive Convolution
AxiomsThe investigation of free additive convolution is a key concept in free probability theory, offering a framework for studying the sum of freely independent random variables. This paper uses free additive convolution and measure dilations to investigate various aspects of Marchenko–Pastur and free Gamma laws in the setting of Cauchy-Stieltjes Kernel ...
Shokrya Saleh Alshqaq +2 more
openaire +2 more sources
Some Limiting Laws in Non-Commutative Probability
AxiomsIn this article, we provide some new limiting laws related to the free multiplicative law of large numbers and involving free and Boolean additive convolutions.
Ayed. R. A. Alanzi +2 more
doaj +1 more source
Local stability of the free additive convolution
Journal of Functional Analysis, 2016 We prove that the system of subordination equations, defining the free additive convolution of two probability measures, is stable away from the edges of the support and blow-up singularities by showing that the recent smoothness condition of Kargin is always satisfied.
Bao, Zhigang +2 more
openaire +3 more sources
On the support of the free additive convolution [PDF]
Journal d'Analyse Mathématique, 2020 We consider the free additive convolution of two probability measures $μ$ and $ν$ on the real line and show that $μ\boxplusν$ is supported on a single interval if $μ$ and $ν$ each has single interval support. Moreover, the density of $μ\boxplusν$ is proven to vanish as a square root near the edges of its support if both $μ$ and $ν$ have power law ...
Bao, Zhigang +2 more
openaire +3 more sources
Aliasing-Free Nonlinear Signal Processing Using Implicitly Defined Functions
IEEE Access, 2022 Digital signal processing relies on the Nyquist-Shannon sampling theorem that applies to and requires a continuous signal with limited bandwidth. However, many systems or networks of signal processing involve nonlinear functions, which could generate new
Emmy S. Wei
doaj +1 more source
On multiplicative conditionally free convolution [PDF]
Transactions of the American Mathematical Society, 2011 Using the combinatorics of non-crossing partitions, we construct a conditionally free analogue of the Voiculescu's S-transform. The result is applied to analytical description of conditionally free multiplicative convolution and characterization of infinite divisibility.
Popa, Mihai, Wang, Jiun-Chau
openaire +2 more sources
MathematicsThis article delves into some properties of free and Boolean multiplicative convolutions, in connection with the theory of Cauchy–Stieltjes kernel (CSK) families and their respective variance functions (VFs).
Fahad Alsharari +2 more
doaj +1 more source
Frontiers in Nutrition, 2022 Sweetener type can influence sensory properties and consumer’s acceptance and preference for low-calorie products. An ideal sweetener does not exist, and each sweetener must be used in situations to which it is best suited. Aspartame and sucralose can be
Gustavo Voltani von Atzingen +5 more
doaj +1 more source
Free convolution operators and free Hall transform
Journal of Functional Analysis, 2013 We define an extension of the polynomial calculus on a W*-probability space by introducing an abstract algebra which contains polynomials. This extension allows us to define transition operators for additive and multiplicative free convolution. It also permits us to characterize the free Segal-Bargmann transform and the free Hall transform introduced ...
openaire +6 more sources
Boolean Cumulants and Subordination in Free Probability
, 2020 We study subordination of free convolutions. We prove that for free random variables $X,Y$ and a Borel function $f$ the conditional expectation $E_\varphi\left[ (z-X-f(X)Yf^*(X))^{-1}| X\right]$, is a resolvent again.
Szpojankowski, Kamil, Lehner, Franz
core +2 more sources