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  • Videos (419)
    Random Matrices and Telecommunications
    01:13:26
    published on November 7, 2016

    Random Matrices and Telecommunications

    By Mérouane Debbah

    IHP

    The asymptotic behaviour of the eigenvalues of large random matrices has been extensively studied since the fifties. One of the first related result was the work of Eugène Wigner in 1955 who remarked that the eigenvalue distribution of a standard Gaussian hermitian matrix converges to a ...

    Appears in collection : Shannon 100

    Score: 38.33892
    Random Matrices and Their Limits
    48:15
    published on November 6, 2017

    Random Matrices and Their Limits

    By Roland Speicher

    IHP

    The free probability perspective on random matrices is that the large size limit of random matrices is given by some (usually interesting) operators on Hilbert spaces and corresponding operator algebras. The prototypical example for this is that independent GUE random matrices converge to free ...

    Appears in collection : Probabilistic techniques and Quantum Information Theory

    Score: 36.382442
    Free probability and random matrices
    published on July 20, 2017

    Free probability and random matrices

    By Philippe Biane

    CIRM

    ... will explain how free probability, which is a theory of independence for non-commutative random variables, can be applied to understand the spectra of various models of random matrices.

    Appears in collection : Mathematical methods of modern statistics / Méthodes mathématiques en statistiques modernes

    Score: 36.289345
    Transfer matrix approach to 1d random band matrices
    53:18
    published on May 9, 2019

    Transfer matrix approach to 1d random band matrices

    By Tatyana Shcherbina

    CIRM

    Random band matrices (RBM) are natural intermediate models to study eigenvalue statistics and quantum propagation in disordered systems, since they interpolate between mean-field type Wigner matrices and random Schrodinger operators. In particular, RBM can be used to model the Anderson metal ...

    Appears in collection : Chaire Jean-Morlet : Equation intégrable aux données initiales aléatoires / Jean-Morlet Chair : Integrable Equation with Random Initial Data

    Score: 33.334484
    On determinants of random matrices
    59:13
    Score: 33.289547
    Random orthogonal polynomials: from matrices to point processes
    42:46
    published on May 9, 2019

    Random orthogonal polynomials: from matrices to point processes

    By Diane Holcomb

    CIRM

    For the commonly studied Hermitian random matrix models there exist tridiagonal matrix models with the same eigenvalue distribution and the same spectral measure $v_{n}$ at the vector $e_{1}$. These tridiagonal matrices give recurrence coefficients that can be used to build the family of random ...

    Appears in collection : Chaire Jean-Morlet : Equation intégrable aux données initiales aléatoires / Jean-Morlet Chair : Integrable Equation with Random Initial Data

    Score: 32.60147
    Compressive sensing with time-frequency structured random matrices
    published on March 16, 2015

    Compressive sensing with time-frequency structured random matrices

    By Holger Rauhut

    CIRM

    ... In particular, we give on overview on recent results on compressive sensing with time-frequency structured random matrices. Keywords: compressive sensing - time-frequency analysis - wavelets - sparsity - random matrices - $\ell_1$-minimization - radar - wireless communications.

    Appears in collections : Special events, 30 Years of Wavelets, 30 years of wavelets / 30 ans des ondelettes

    Score: 30.84433
    Moments of random matrices and hypergeometric orthogonal polynomials
    51:34
    published on May 9, 2019

    Moments of random matrices and hypergeometric orthogonal polynomials

    By Francesco Mezzadri

    CIRM

    We establish a new connection between moments of n×n random matrices $X_{n}$ and hypergeometric orthogonal polynomials. Specifically, we consider moments $\mathbb{E}\mathrm{Tr} X_n^{-s}$ as a function of the complex variable $s\in\mathbb{C}$, whose analytic structure we describe completely. We ...

    Appears in collection : Chaire Jean-Morlet : Equation intégrable aux données initiales aléatoires / Jean-Morlet Chair : Integrable Equation with Random Initial Data

    Score: 30.502972
  • Collections (36)
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