On Riesz distribution

Dı́az-Garcı́a, José A.

doi:10.1007/s00184-013-0449-5

Cited by 5 publications

(2 citation statements)

References 28 publications

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“…Remark 2.4. The paper [14], Theorem 2 with β = 1 and Σ = I claims a formula for the eigenvalue PDF of (1.1). However this is incorrect due to its reliance on the erroneous Eq.…”

Section: 13)mentioning

confidence: 99%

Muttalib–Borodin ensembles in random matrix theory — realisations and correlation functions

Forrester¹,

Wang²

2017

Electron. J. Probab.

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Muttalib-Borodin ensembles are characterised by the pair interaction term in the eigenvalue probability density function being of the formWe study the Laguerre and Jacobi versions of this model -so named by the form of the one-body interaction termsand show that for θ ∈ Z + they can be realised as the eigenvalue PDF of certain random matrices with Gaussian entries. For general θ > 0, realisations in terms of the eigenvalue PDF of ensembles involving triangular matrices are given. In the Laguerre case this is a recent result due to Cheliotis, although our derivation is different. We make use of a generalisation of a double contour integral formula for the correlation functions contained in a paper by Adler, van Moerbeke and Wang to analyse the global density (which we also analyse by studying characteristic polynomials), and the hard edge scaled correlation functions. For the global density functional equations for the corresponding resolvents are obtained; solving this gives the moments in terms of Fuss-Catalan numbers (Laguerre case -a known result) and particular binomial coefficients (Jacobi case). For θ ∈ Z + the Laguerre and Jacobi cases are closely related to the squared singular values for products of θ standard Gaussian random matrices, and truncations of unitary matrices, respectively. At the hard edge the double contour integral formulas provide a double contour integral form of the scaled correlation kernel obtained by Borodin in terms of Wright's Bessel function.

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“…Remark 2.4. The paper [14], Theorem 2 with β = 1 and Σ = I claims a formula for the eigenvalue PDF of (1.1). However this is incorrect due to its reliance on the erroneous Eq.…”

Section: 13)mentioning

confidence: 99%

Muttalib–Borodin ensembles in random matrix theory — realisations and correlation functions

Forrester¹,

Wang²

2017

Electron. J. Probab.

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“…In 2013, Corma and co-workers designed a bifunctional cinchona-and propylamine-based organocatalyst (XVIII, Scheme 16) using a sol-gel synthesis catalyzed by very small amounts of NH 4 F in the absence of structural directing agents, at low temperature and at neutral pH, [64] to obtain the hybrid organic-inorganic mesoporous material. This catalyst has been tested in the multicomponent reaction between aldehydes, nitromethane and malonates in a one-pot combined Henry condensation and Michael-type addition to obtain the optically adducts 11 b-n.…”

Section: Thioureas Supported On Mesoporous Silicamentioning

confidence: 99%

Recent Developments on Supported Hydrogen‐bond Organocatalysts

Franconetti

Gonzalo

2018

ChemCatChem

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Hydrogen‐bond organocatalysts are a family of Brønsted acid organic compounds able to activate electrophilic substrates toward nucleophilic addition through hydrogen bonding interactions. Since the first report using these catalysts, they have been widely exploited in several valuable processes, in general with high activities and selectivities. The immobilization of hydrogen‐bond catalysts affords heterogeneous systems which enable different features for a green chemistry approach, such as chemical and mechanical stability, easy work‐up and/or reusability. Several kinds of supports have been employed for immobilization while maintaining the advantages of the homogeneous catalysts. In the present review, we have mainly focused our attention in the immobilization of ureas, thioureas and squaramides organocatalysts onto various supports, including polymeric materials, mesoporous silicas, nanoparticles and ionic liquids, and also some copolymerization processes have been described. In addition, the role of these supported organocatalysts published since 2010 on different stereoselective transformations has been evaluated.

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An expectation maximization algorithm for the hidden markov models with multiparameter student-t observations

Ghorbel,

Louati

2023

Comput Stat

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On Riesz distribution

Abstract: The Riesz distribution for real normed division algebras is derived in this work. Then two versions of these distributions are proposed and some of their properties are studied.

Cited by 5 publications

References 28 publications

Muttalib–Borodin ensembles in random matrix theory — realisations and correlation functions

Muttalib–Borodin ensembles in random matrix theory — realisations and correlation functions

Recent Developments on Supported Hydrogen‐bond Organocatalysts

An expectation maximization algorithm for the hidden markov models with multiparameter student-t observations

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