Pérez-Sánchez, Carlos I
Published in
Letters in mathematical physics

We focus on functional renormalization for ensembles of several (say n ≥ 1 ) random matrices, whose potentials include multi-traces, to wit, the probability measure contains factors of the form exp [ - Tr ( V 1 ) × ⋯ × Tr ( V k ) ] for certain noncommutative polynomials V 1 , … , V k ∈ C ⟨ n ⟩ in the n matrices. This article shows how the "algebra ...

Duchemin, Quentin De Castro, Yohann

The Random Geometric Graph (RGG) is a random graph model for network data with an underlying spatial representation. Geometry endows RGGs with a rich dependence structure and often leads to desirable properties of real-world networks such as the small-world phenomenon and clustering. Originally introduced to model wireless communication networks, R...

Ha, Gao Fan Zhang, Qiuyan Bai, Zhidong Wang, You Gan

In this paper, a ridgelized Hotelling's *T*^{2} test is developed for a hypothesis on a large-dimensional mean vector under certain moment conditions. It generalizes the main result of Chen *et al.* [A regularized Hotelling's *t*^{2} test for pathway analysis in proteomic studies, *J. Am. Stat. Assoc.* 106(496) (2011) 1345-1360.] by relaxing their Gaussian assum...

Rosuel, Alexis

Large random matrices have been proved to be of fundamental importance in mathematics (high dimensional probability, operator algebras, combinatorics, number theory,...) and in physics (nuclear physics, quantum fields theory, quantum chaos,..) for a long time. The use of large random matrices is more recent in statistical signal processing and time...

Gautié, Tristan

This statistical physics thesis focuses on the study of three kinds of systems which display repulsive interactions: eigenvalues of random matrices, non-crossing random walks and trapped fermions. These systems share many links, which can be exhibited not only at the level of their static version, but also at the level of their dynamical version. W...

Prod'homme, Maxime

This thesis deals with the optimal transport problem, in particular with regularity properties shared by optimal transport maps. The first part of this manuscript provides a new proof of the Caffarelli contraction theorem, stating that the optimal transport map from the gaussian measure to a measure with a uniformly log-concave density with respect...

Chèze, Guillaume

In this article we propose a probabilistic framework in order to study the fair division of a divisible good, e.g. a cake, between n players. Our framework follows the same idea than the "Full independence model" used in the study of fair division of indivisible goods. We show that, in this framework, there exists an envy-free division algorithm sa...

Parraud, Félix

This PhD lies at the intersection of Random Matrix Theory and Free Probability Theory. The connection between those two fields dates back to the early nineties with the work of Voiculescu who created the Theory of free probability. A probability theory for noncommutative variables where the notion of freeness replaces the one of independence in cla...

Kahn, Ezéchiel

This thesis is motivated by the study of covariance matrices, and is naturally structured in three parts. In the first part, we study dynamic models related to covariance matrices. More precisely, we study the systems of stochastic differential equations inherited from the dynamics of the eigenvalues of matrix valued processes named the Wishart pro...

Kahn, Ezechiel

Cette thèse est motivée par l'étude des matrices de covariance, et s'articule naturellement en trois parties. Dans la première partie, nous étudions des modèles dynamiques liés aux matrices de covariance. Nous étudions plus précisément les systèmes d'équations différentielles stochastiques hérités de la dynamique des valeurs propres de processus ma...