Free probability meets topological recursion [PDF]
, 2023 The subject of this thesis lies at the intersection of free probability, Hurwitz theory and topological recursion. It is based on the following collaborations: Higher order free probability vs.
Leid, Felix
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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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DISCRETE INTERPOLATION BETWEEN MONOTONE PROBABILITY AND FREE PROBABILITY [PDF]
Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2006 We construct a sequence of states called m-monotone product states which give a discrete interpolation between the monotone product of states of Muraki in monotone probability and the free product of states of Avitzour and Voiculescu in free probability.
Lenczewski, Romuald, Sałapata, Rafał
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Primes in Intervals and Semicircular Elements Induced by p-Adic Number Fields
Mathematics, 2019 In this paper, we study free probability on (weighted-)semicircular elements in a certain Banach *-probability space ( LS , τ 0 ) induced by measurable functions on p-adic number fields Q p over primes p .
Ilwoo Cho, Palle Jorgensen
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Free probability induced by electric resistance networks on energy Hilbert spaces [PDF]
Opuscula Mathematica, 2011 We show that a class of countable weighted graphs arising in the study of electric resistance networks (ERNs) are naturally associated with groupoids.
Ilwoo Cho, Palle E. T. Jorgensen
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Operation State Evaluation Method of Smart Distribution Network Based on Free Probability Theory
Frontiers in Energy Research, 2022 In view of the current situation that the new generation of smart grids with “double high” characteristics is in urgent need of effective state evaluation methods due to the characteristics of strong volatility and diverse demands, a method of operation ...
Jiaxin Zhang +6 more
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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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FREE PROBABILITY FOR PROBABILISTS [PDF]
, 2010 This is an introduction to some of the most probabilistic aspects of free probability theory.
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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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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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