The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
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...
The brownian motion model introduced by Dyson [7] for the eigenvalues of unitary random matrices is interpreted as a system of 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 goes to infinity (through the empirical measure process). We prove that a limiting...
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...
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.
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...
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.
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.
Currently displaying 1 –
20 of
23