Results 21 to 30 of about 8,503,072 (299)
Duality for Optimal Couplings in Free Probability [PDF]
Communications in Mathematical Physics, 2021 We study the free probabilistic analog of optimal couplings for the quadratic cost, where classical probability spaces are replaced by tracial von Neumann algebras, and probability measures on Rm\documentclass[12pt]{minimal} \usepackage{amsmath ...
W. Gangbo +3 more
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Cumulant–Cumulant Relations in Free Probability Theory from Magnus’ Expansion [PDF]
Foundations of Computational Mathematics, 2020 Relations 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 ...
Adrian Celestino +3 more
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Hopf algebras and the logarithm of the S-transform in free probability ― Extended abstract [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 This document is an extended abstract of the paper `Hopf algebras and the logarithm of the S-transform in free probability' in which we introduce a Hopf algebraic approach to the study of the operation $\boxtimes$ (free multiplicative convolution) from ...
Mitja Mastnak, Alexandru Nica
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Certain group dynamical systems induced by Hecke algebras [PDF]
Opuscula Mathematica, 2016 In this paper, we study dynamical systems induced by a certain group \(\mathfrak{T}_{N}^{K}\) embedded in the Hecke algebra \(\mathcal{H}(G_{p})\) induced by the generalized linear group \(G_{p} = GL_{2}(\mathbb{Q}_{p})\) over the \(p\)-adic number ...
Ilwoo Cho
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Deformation of semicircular and circular laws via p-adic number fields and sampling of primes [PDF]
Opuscula Mathematica, 2019 In this paper, we study semicircular elements and circular elements in a certain Banach \(*\)-probability space \((\mathfrak{LS},\tau ^{0})\) induced by analysis on the \(p\)-adic number fields \(\mathbb{Q}_{p}\) over primes \(p\).
Ilwoo Cho, Palle E. T. Jorgensen
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Parameter-free Regret in High Probability with Heavy Tails [PDF]
Neural Information Processing Systems, 2022 We present new algorithms for online convex optimization over unbounded domains that obtain parameter-free regret in high-probability given access only to potentially heavy-tailed subgradient estimates.
Jiujia Zhang, Ashok Cutkosky
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Banach-Space Operators Acting on Semicircular Elements Induced by p-Adic Number Fields over Primes p
Mathematics, 2019 In this paper, we study certain Banach-space operators acting on the Banach *-probability space ( LS , τ 0 ) generated by semicircular elements Θ p , j induced by p-adic number fields Q p over the set P of all
Ilwoo Cho
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Sums of commutators in free probability [PDF]
Journal of Functional Analysis, 2021 We study the linear span of commutators of free random variables and show that these are the only quadratic forms which satisfy the following equivalent properties: * preservation free infinite divisibility * free and strong cancellation of odd cumulants * symmetric distribution for any free family.
Wiktor Ejsmont, Franz Lehner
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Acting Semicircular Elements Induced by Orthogonal Projections on Von-Neumann-Algebras
Mathematics, 2017 In this paper, we construct a free semicircular family induced by Z -many mutually-orthogonal projections, and construct Banach ∗-probability spaces ...
Ilwoo Cho
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Shuffle group laws: applications in free probability [PDF]
Proceedings of the London Mathematical Society, 2017 Commutative shuffle products are known to be intimately related to universal formulas for products, exponentials and logarithms in group theory as well as in the theory of free Lie algebras, such as, for instance, the Baker–Campbell–Hausdorff formula or ...
K. Ebrahimi-Fard, F. Patras
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