40 citations · 137 across the 14 of their papers we have counts for
14 papers
The continuum limit of some products of random matrices associated with renewing flows
Yves Tourigny
We consider the continuum limit of some products of random matrices in that arise as discretisations of incompressible renewing flows -- that is, of flow…
The generalized Lyapunov exponent for the one-dimensional Schrödinger equation with Cauchy disorder: some exact results
Alain Comtet, Christophe Texier, Yves Tourigny
We consider the one-dimensional Schrödinger equation with a random potential and study the cumulant generating function of the logarithm of the wave function , known in the l…
Representation theory and products of random matrices in
Alain Comtet, Christophe Texier, Yves Tourigny
The statistical behaviour of a product of independent, identically distributed random matrices in is encoded in the generalised Lyapunov exponent ; th…
Impurity models and products of random matrices
Alain Comtet, Yves Tourigny
This is an introduction to the theory of one-dimensional disordered systems and products of random matrices, confined to the 2 by 2 case. The notion of impurity model--- that is, a…
Explicit formulae in probability and in statistical physics
Alain Comtet, Yves Tourigny
We consider two aspects of Marc Yor's work that have had an impact in statistical physics: firstly, his results on the windings of planar Brownian motion and their implications for…
One-dimensional disordered quantum mechanics and Sinai diffusion with random absorbers
Aurélien Grabsch, Christophe Texier, Yves Tourigny
We study the one-dimensional Schrödinger equation with a disordered potential of the form where is a Gaussian white noise with mean and v…
The Lyapunov exponent of products of random matrices close to the identity
A. Comtet, J. M. Luck, C. Texier +1
We study products of arbitrary random real matrices that are close to the identity matrix. Using the Iwasawa decomposition of , we identify a…
Lyapunov exponents, one-dimensional Anderson localisation and products of random matrices
Alain Comtet, Christophe Texier, Yves Tourigny
The concept of Lyapunov exponent has long occupied a central place in the theory of Anderson localisation; its interest in this particular context is that it provides a reasonable…
Supersymmetric quantum mechanics with Levy disorder in one dimension
Alain Comtet, Christophe Texier, Yves Tourigny
We consider the Schroedinger equation with a supersymmetric random potential, where the superpotential is a Levy noise. We focus on the problem of computing the so-called complex L…
Continued fraction solution of Krein's inverse problem
Yves Tourigny
The spectral data of a vibrating string are encoded in its so-called characteristic function. We consider the problem of recovering the distribution of mass along the string from i…
Products of random matrices and generalised quantum point scatterers
Alain Comtet, Christophe Texier, Yves Tourigny
To every product of matrices, there corresponds a one-dimensional Schrödinger equation whose potential consists of generalised point scatterers. Products of {\em random}…
Excursions of diffusion processes and continued fractions
Alain Comtet, Yves Tourigny
It is well-known that the excursions of a one-dimensional diffusion process can be studied by considering a certain Riccati equation associated with the process. We show that, in m…
Pade approximants of random Stieltjes series
Jens Marklof, Yves Tourigny, Lech Wolowski
We consider the random continued fraction S(t) := 1/(s_1 + t/(s_2 + t/(s_3 + >...))) where the s_n are independent random variables with the same gamma distribution. For every real…
Explicit invariant measures for products of random matrices
Jens Marklof, Yves Tourigny, Lech Wolowski
We construct explicit invariant measures for a family of infinite products of random, independent, identically-distributed elements of SL(2,C). The matrices in the product are such…