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### A recursion formula for the moments of the gaussian orthogonal ensemble

Annales de l'I.H.P. Probabilités et statistiques

We present an analogue of the Harer–Zagier recursion formula for the moments of the gaussian Orthogonal Ensemble in the form of a five term recurrence equation. The proof is based on simple gaussian integration by parts and differential equations on Laplace transforms. A similar recursion formula holds for the gaussian Symplectic Ensemble. As in the complex case, the result is interpreted as a recursion formula for the number of 1-vertex maps in locally orientable surfaces with a given number of...

### Another look at the moment method for large dimensional random matrices.

Electronic Journal of Probability [electronic only]

### Brownian particles with electrostatic repulsion on the circle : Dyson’s model for unitary random matrices revisited

ESAIM: Probability and Statistics

The brownian motion model introduced by Dyson [7] for the eigenvalues of unitary random matrices $N×N$ is interpreted as a system of $N$ interacting brownian particles on the circle with electrostatic inter-particles repulsion. The aim of this paper is to define the finite particle system in a general setting including collisions between particles. Then, we study the behaviour of this system when the number of particles $N$ goes to infinity (through the empirical measure process). We prove that a limiting...

### Brownian particles with electrostatic repulsion on the circle: Dyson's model for unitary random matrices revisited

ESAIM: Probability and Statistics

The Brownian motion model introduced by Dyson [7] for the eigenvalues of unitary random matrices N x N is interpreted as a system of N interacting Brownian particles on the circle with electrostatic inter-particles repulsion. The aim of this paper is to define the finite particle system in a general setting including collisions between particles. Then, we study the behaviour of this system when the number of particles N goes to infinity (through the empirical measure process). We prove...

### Determinantal processes and independence.

Probability Surveys [electronic only]

### Dichotomy in a scaling limit under Wiener measure with density.

Electronic Communications in Probability [electronic only]

### Different approaches to stochastic parabolic differential equations

Proceedings of the 10th Winter School on Abstract Analysis

### Differential operators and spectral distributions of invariant ensembles from the classical orthogonal polynomials. The continuous case.

Electronic Journal of Probability [electronic only]

### Dissipative systems

Proceedings of the 12th Winter School on Abstract Analysis

### Fonction de Correlation pour des Mesures Complexes

Séminaire Équations aux dérivées partielles

We study a class of holomorphic complex measures, which are close in an appropriate sense to a complex Gaussian. We show that these measures can be reduced to a product measure of real Gaussians with the aid of a maximum principle in the complex domain. The formulation of this problem has its origin in the study of a certain class of random Schrödinger operators, for which we show that the expectation value of the Green’s function decays exponentially.

### Gaussian solutions to the lagrangian variational problem in stochastic mechanics

Annales de l'I.H.P. Physique théorique

### Hermitian, symmetric and symplectic random ensembles: PDEs for the distribution of the spectrum.

Annals of Mathematics. Second Series

### Nonlinear filtering for observations on a random vector field along a random path. Application to atmospheric turbulent velocities

ESAIM: Mathematical Modelling and Numerical Analysis

To filter perturbed local measurements on a random medium, a dynamic model jointly with an observation transfer equation are needed. Some media given by PDE could have a local probabilistic representation by a Lagrangian stochastic process with mean-field interactions. In this case, we define the acquisition process of locally homogeneous medium along a random path by a Lagrangian Markov process conditioned to be in a domain following the path and conditioned to the observations. The nonlinear...

### Random matrices and permutations, matrix integrals and integrable systems

Séminaire Bourbaki

### Rigorous solution of a mean field spin glass model.

Journal of Applied Mathematics and Stochastic Analysis

### Stochastic Solution of a KPP-Type Nonlinear Fractional Differential Equation

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 26A33, 76M35, 82B31A stochastic solution is constructed for a fractional generalization of the KPP (Kolmogorov, Petrovskii, Piskunov) equation. The solution uses a fractional generalization of the branching exponential process and propagation processes which are spectral integrals of Levy processes.

### Strict inequality for phase transition between ferromagnetic and frustrated systems.

Electronic Journal of Probability [electronic only]

### The rate of convergence for spectra of GUE and LUE matrix ensembles

Open Mathematics

We obtain optimal bounds of order O(n −1) for the rate of convergence to the semicircle law and to the Marchenko-Pastur law for the expected spectral distribution functions of random matrices from the GUE and LUE, respectively.

### The stochastic limit in the analysis of some modified open BCS models

Banach Center Publications

### Transfer operator for piecewise affine approximations of interval maps

Annales de l'I.H.P. Physique théorique

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