A rigorous introduction to the statistical analysis of random functions and associated random operators. Viewing random functions either as random Hilbert vectors or as stochastic processes, we will see the interplay between nonparametrics and multivariate ...
This course is an introduction to the spectral theory of linear operators acting in Hilbert spaces. The main goal is the spectral decomposition of unbounded selfadjoint operators. We will also give elementary applications to quantum mechanics. ...
Ce cours ambitionne de présenter les mathématiques de la mécanique quantique, et plus généralement de la physique quantique. Il s'adresse essentiellement aux physiciens, ou a des mathématiciens intéressés dans le domaine. ...
We cover the theory and applications of sparse stochastic processes (SSP). SSP are solutions of differential equations driven by non-Gaussian innovations. They admit a parsimonious representation in a wavelet basis and are relevant to coding, compressed se ...
The aim of this doctoral course by Nicolas Sangouard is to lay the theoretical groundwork that is needed for students to understand how to take advantage of quantum effects for communication technologies and contribute to on-going efforts in this field. ...
The course will focus on a probabilistic construction of a conformal field theory related to random Riemann surfaces, called the Liouville conformal field theory. The symmetries of the theory allow to express the n-point correlation functions in terms of 3 ...
Non-positive curvature is a fundamental aspect of geometry appearing in Euclidean spaces, hyperbolic spaces, trees, buildings and many more spaces. We study it with the general but powerful tool of CA ...
This course is intended for students who want to understand modern large-scale data analysis systems and database systems. It covers a wide range of topics and technologies, and will prepare students to be able to build such systems as well as read and und ...
Quantum mechanics is one of the most successful physical theories. This course presents the mathematical formalism (functional analysis and spectral theory) that underlies quantum mechanics. It is simultaneously an introduction to mathematical physics and ...