Publications associées à Complex random variable

Global eigenvalue distribution of matrices defined by the skew-shift

We consider large Hermitian matrices whose entries are defined by evaluating the exponential function along orbits of the skew-shift

\binom{j}{2} \omega+jy+x \mod 1

for irrational

\omega

. We prove that the eigenvalue distribution of these matrices conv ...

2019

The Mutual Information in Random Linear Estimation Beyond i.i.d. Matrices

Nicolas Macris, Florent Gérard Krzakala, Jean François Emmanuel Barbier

There has been definite progress recently in proving the variational single-letter formula given by the heuristic replica method for various estimation problems. In particular, the replica formula for the mutual information in the case of noisy linear esti ...

IEEE2018

A Posteriori Error Estimation for the Stochastic Collocation Finite Element Method

Fabio Nobile, Diane Sylvie Guignard

In this work, we consider an elliptic partial differential equation (PDE) with a random coefficient solved with the stochastic collocation finite element method (SC-FEM). The random diffusion coefficient is assumed to depend in an affine way on independent ...

2018

Chebyshev Inequalities for Products of Random Variables

Daniel Kuhn, Napat Rujeerapaiboon, Wolfram Wiesemann

We derive sharp probability bounds on the tails of a product of symmetric non-negative random variables using only information about their first two moments. If the covariance matrix of the random variables is known exactly, these bounds can be computed nu ...

2018

A posteriori error estimation for the steady Navier-Stokes equations in random domains

Fabio Nobile, Marco Picasso, Diane Sylvie Guignard

We consider finite element error approximations of the steady incompressible Navier-Stokes equations defined on a randomly perturbed domain, the perturbation being small. Introducing a random mapping, these equations are transformed into PDEs on a fixed re ...

Elsevier2017

Reconstruction using approximate message passing methods

Paul Hurley, Matthieu Martin Jean-André Simeoni, Giovanni Cherubini, Sanaz Kazemi

The present invention is notably directed to a computer-implemented method for image reconstruction. The method comprises: accessing elements that respectively correspond to measurement values, which can be respectively mapped to measurement nodes; and per ...

2017

MATHICSE Technical Report : A posteriori error estimation for the stochastic collocation finite element method

Fabio Nobile, Diane Sylvie Guignard

In this work, we consider an elliptic partial differential equation with a random coefficient solved with the stochastic collocation finite element method. The random diffusion coefficient is assumed to depend in an affine way on independent random variabl ...

MATHICSE2017

Harder, Better, Faster, Stronger Convergence Rates for Least-Squares Regression

Nicolas Henri Bernard Flammarion, Aymeric Daphnis Kévin Dieuleveut

We consider the optimization of a quadratic objective function whose gradients are only accessible through a stochastic oracle that returns the gradient at any given point plus a zero-mean finite variance random error. We present the first algorithm that a ...

2017

Bridging asymptotic independence and dependence in spatial extremes using Gaussian scale mixtures

Emeric Rolland Georges Thibaud, Raphaël Huser

Gaussian scale mixtures are constructed as Gaussian processes with a random variance. They have non-Gaussian marginals and can exhibit asymptotic dependence unlike Gaussian processes, which are asymptotically independent except in the case of perfect depen ...

Elsevier Sci Ltd2017

Symplectic Dynamical Low Rank approximation of wave equations with random parameters

Fabio Nobile, Eleonora Musharbash

In this paper we propose a dynamical low-rank strategy for the approximation of second order wave equations with random parameters. The governing equation is rewritten in Hamiltonian form and the approximate solution is expanded over a set of

2S

dynamica ...

2017

Complex random variable

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Global eigenvalue distribution of matrices defined by the skew-shift

The Mutual Information in Random Linear Estimation Beyond i.i.d. Matrices

A Posteriori Error Estimation for the Stochastic Collocation Finite Element Method

Chebyshev Inequalities for Products of Random Variables

A posteriori error estimation for the steady Navier-Stokes equations in random domains

Reconstruction using approximate message passing methods

MATHICSE Technical Report : A posteriori error estimation for the stochastic collocation finite element method

Harder, Better, Faster, Stronger Convergence Rates for Least-Squares Regression

Bridging asymptotic independence and dependence in spatial extremes using Gaussian scale mixtures

Symplectic Dynamical Low Rank approximation of wave equations with random parameters

A Posteriori Error Estimation for the Stochastic Collocation Finite Element Method

MATHICSE Technical Report : A posteriori error estimation for the stochastic collocation finite element method

Global eigenvalue distribution of matrices defined by the skew-shift

Chebyshev Inequalities for Products of Random Variables

A posteriori error estimation for the steady Navier-Stokes equations in random domains

Reconstruction using approximate message passing methods

Harder, Better, Faster, Stronger Convergence Rates for Least-Squares Regression

Bridging asymptotic independence and dependence in spatial extremes using Gaussian scale mixtures

Symplectic Dynamical Low Rank approximation of wave equations with random parameters

The Mutual Information in Random Linear Estimation Beyond i.i.d. Matrices