Results 11 to 20 of about 13,504 (178)
Generalized free cumulants for quantum chaotic systems
Journal of High Energy PhysicsThe eigenstate thermalization hypothesis (ETH) is the leading conjecture for the emergence of statistical mechanics in generic isolated quantum systems and is formulated in terms of the matrix elements of operators.
Siddharth Jindal, Pavan Hosur
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Free cumulants, Schr\"oder trees, and operads
Advances in Applied Mathematics, 2017 The functional equation defining the free cumulants in free probability is lifted successively to the noncommutative Fa\`a di Bruno algebra, and then to the group of a free operad over Schr\"oder trees.
Josuat-Vergès, Matthieu +3 more
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On the computation of classical, boolean and free cumulants [PDF]
Applied Mathematics and Computation, 2008 This paper introduces a simple and computationally efficient algorithm for conversion formulae between moments and cumulants. The algorithm provides just one formula for classical, boolean and free cumulants.
Di Nardo, E., Oliva, I.
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Monotone, free, and boolean cumulants: a shuffle algebra approach [PDF]
Advances in Mathematics, 2018 The theory of cumulants is revisited in the "Rota way", that is, by following a combinatorial Hopf algebra approach. Monotone, free, and boolean cumulants are considered as infinitesimal characters over a particular combinatorial Hopf algebra. The latter
Ebrahimi-Fard, Kurusch, Patras, Frederic
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Star-cumulants of free unitary Brownian motion
Advances in Applied Mathematics, 2015 We study joint free cumulants of u_t and u_t^{*}, where u_t is a free unitary Brownian motion at time t. We determine explicitly some special families of such cumulants.
Demni, Nizar +2 more
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Cumulant–Cumulant Relations in Free Probability Theory from Magnus’ Expansion [PDF]
Foundations of Computational Mathematics, 2021 AbstractRelations between moments and cumulants play a central role in both classical and non-commutative probability theory. The latter allows for several distinct families of cumulants corresponding to different types of independences: free, Boolean and monotone. Relations among those cumulants have been studied recently.
Patras, Frédéric +3 more
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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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Model-Free Forward Screening Via Cumulative Divergence [PDF]
Journal of the American Statistical Association, 2019 Feature screening plays an important role in the analysis of ultrahigh dimensional data. Due to complicated model structure and high noise level, existing screening methods often suffer from model misspecification and the presence of outliers. To address these issues, we introduce a new metric named cumulative divergence (CD), and develop a CD-based ...
Tingyou Zhou +3 more
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Cumulants for finite free convolution [PDF]
Journal of Combinatorial Theory, Series A, 2018 In this paper we define cumulants for finite free convolution. We give a moment-cumulant formula and show that these cumulants satisfy desired properties: they are additive with respect to finite free convolution and they approach free cumulants as the dimension goes to infinity.
Arizmendi, Octavio, Perales, Daniel
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Free probability on Hecke algebras and certain group C^{*}-algebras induced by Hecke algebras [PDF]
Opuscula Mathematica, 2016 In this paper, by establishing free-probabilistic models on the Hecke algebras \(\mathcal{H}\left(GL_{2}(\mathbb{Q}_{p})\right)\) induced by \(p\)-adic number fields \(\mathbb{Q}_{p}\), we construct free probability spaces for all primes \(p\).
Ilwoo Cho
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