Results 21 to 30 of about 3,383,288 (169)
Dual Garside structure of braids and free cumulants of products [PDF]
, 2014 We count the n-strand braids whose normal decomposition has length at most two in the dual braid monoid B_n+* by reducing the question to a computation of free cumulants for a product of independent variables, for which we establish a general formula.
Biane, Philippe, Dehornoy, Patrick
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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.
Adrian Celestino +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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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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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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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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Rank one HCIZ at high temperature: interpolating between classical and free convolutions
SciPost Physics, 2022 We study the rank one Harish-Chandra-Itzykson-Zuber integral in the limit where $\frac{N \beta}{2} \to c $, called the high temperature regime and show that it can be used to construct a promising one-parameter interpolation, with parameter $c ...
Pierre Mergny, Marc Potters
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${\epsilon}$ -Noncrossing Partitions and Cumulants in Free Probability [PDF]
International Mathematics Research Notices, 2017 Motivated by recent work on mixtures of classical and free probabilities, we introduce and study the notion of $ε$-noncrossing partitions. It is shown that the set of such partitions forms a lattice, which interpolates as a poset between the poset of partitions and the one of noncrossing partitions.
Ebrahimi-Fard, Kurusch +2 more
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Cumulants of the QCD topological charge distribution
Physics Letters B, 2015 The distribution of the QCD topological charge can be described by cumulants, with the lowest one being the topological susceptibility. The vacuum energy density in a θ-vacuum is the generating function for these cumulants.
Feng-Kun Guo, Ulf-G. Meißner
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A New Look at the Coefficients of a Reciprocal Generating Function
The Scientific World Journal, 2014 We study a special property of free cumulants. We prove that coefficients of a reciprocal generating function correspond to “free cumulants with the first two elements in the same block.”
Wiktor Ejsmont
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