Results 21 to 30 of about 5,158,059 (301)
Sample variance in free probability
Journal of Functional Analysis, 2017 Let $X_1, X_2,\dots, X_n$ denote i.i.d.~centered standard normal random variables, then the law of the sample variance $Q_n=\sum_{i=1}^n(X_i-\bar{X})^2$ is the $χ^2$-distribution with $n-1$ degrees of freedom. It is an open problem in classical probability to characterize all distributions with this property and in particular, whether it characterizes ...
Wiktor Ejsmont, Franz Lehner
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Krein-space operators determined by free product algebras induced by primes and graphs
Special Matrices, 2017 In this paper, we introduce certain Krein-space operators induced by free product algebras induced by both primes and directed graphs. We study operator-theoretic properties of such operators by computing free-probabilistic data containing number ...
Cho Ilwoo, Jorgensen Palle E. T.
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Classical and Free Cumulants of the ω-Gaussian Central Limit Law
MathematicsWe study the classical and free cumulants of the ω-Gaussian central limit laws arising from braidable quantum coin tosses. Taking the known central limit theorem and oriented-pairing moment formula as input, we carry out a cumulant-level analysis of the ...
Ayman Alahmade
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Coherent Fluctuations in Noisy Mesoscopic Systems, the Open Quantum SSEP, and Free Probability
Physical Review X, 2023 Quantum coherences characterize the ability of particles to quantum mechanically interfere within some given distances. In the context of noisy many-body quantum systems, these coherences can fluctuate. A simple toy model to study such fluctuations in an
Ludwig Hruza, Denis Bernard
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Boolean cumulants and subordination in free probability [PDF]
Random Matrices: Theory and Applications, 2020 Subordination is the basis of the analytic approach to free additive and multiplicative convolution. We extend this approach to a more general setting and prove that the conditional expectation [Formula: see text] for free random variables [Formula: see text] and a Borel function [Formula: see text] is a resolvent again.
Franz Lehner, Kamil Szpojankowski
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, 2015 This article focuses on free probability theory, which is useful for dealing with asymptotic eigenvalue distributions in situations involving several matrices. In particular, it considers some of the basic ideas and results of free probability theory, mostly from the random matrix perspective.
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Jurnal Penelitian Fisika dan Aplikasinya, 2022 Solving the Schrödinger equation may result in a wave function of a particle in a quantum system, which can afford the information with respect to the particle’s behavior.
Sri Purwaningsih, Ramacos Fardela
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Spectrum Concentration in Deep Residual Learning: A Free Probability Approach
IEEE Access, 2019 We revisit the weight initialization of deep residual networks (ResNets) by introducing a novel analytical tool in free probability to the community of deep learning.
Zenan Ling, Robert C. Qiu
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Union-free Hypergraphs and Probability Theory
European Journal of Combinatorics, 1984 This paper contains new lower and upper bounds on the number of subsets of an n element set one can have so that the union of no two equals that of two others. A new lower bound is obtained when no two unions of any kind are the same; and a new upper bound when no set has the same union with two others.
Peter Frankl, Zoltán Füredi
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Hyperosmotic stress induces PARP1‐mediated HPF1‐dependent mono(ADP‐ribosyl)ation
FEBS Letters, EarlyView.Sorbitol‐induced hyperosmotic stress rapidly induces reversible mono(ADP‐ribosyl)ation (MARylation) on PARP1 without the signs of genotoxic signaling. We show that PARP1 autoMARylation is HPF1 dependent and forms hydroxylamine‐resistant O‐glycosidic linkages.
Anna Georgina Kopasz +11 more
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