Algebraic combinatorics | Multilinear algebra | Theorems
Gamas's theorem is a result in multilinear algebra which states the necessary and sufficient conditions for a tensor symmetrized by an irreducible representation of the symmetric group to be zero. It was proven in 1988 by Carlos Gamas. Additional proofs have been given by Pate and Berget. (Wikipedia).
(PP 6.3) Gaussian coordinates does not imply (multivariate) Gaussian
An example illustrating the fact that a vector of Gaussian random variables is not necessarily (multivariate) Gaussian.
From playlist Probability Theory
(ML 19.2) Existence of Gaussian processes
Statement of the theorem on existence of Gaussian processes, and an explanation of what it is saying.
From playlist Machine Learning
Joe Neeman: Gaussian isoperimetry and related topics II
The Gaussian isoperimetric inequality gives a sharp lower bound on the Gaussian surface area of any set in terms of its Gaussian measure. Its dimension-independent nature makes it a powerful tool for proving concentration inequalities in high dimensions. We will explore several consequence
From playlist Winter School on the Interplay between High-Dimensional Geometry and Probability
(PP 6.5) Affine property, Constructing Gaussians, and Sphering
Any affine transformation of a (multivariate) Gaussian random variable is (multivariate) Gaussian. How to construct any (multivariate) Gaussian using an affine transformation of standard normals. How to "sphere" a Gaussian, i.e. transform it into a vector of independent standard normals.
From playlist Probability Theory
Gaussian Integral 7 Wallis Way
Welcome to the awesome 12-part series on the Gaussian integral. In this series of videos, I calculate the Gaussian integral in 12 different ways. Which method is the best? Watch and find out! In this video, I calculate the Gaussian integral by using a technique that is very similar to the
From playlist Gaussian Integral
Theory of numbers: Gauss's lemma
This lecture is part of an online undergraduate course on the theory of numbers. We describe Gauss's lemma which gives a useful criterion for whether a number n is a quadratic residue of a prime p. We work it out explicitly for n = -1, 2 and 3, and as an application prove some cases of Di
From playlist Theory of numbers
[BOURBAKI 2017] 21/10/2017 - 4/4 - Serge CANTAT
Progrès récents concernant le programme de Zimmer [d'après A. Brown, D. Fisher, et S. Hurtado] ---------------------------------- Vous pouvez nous rejoindre sur les réseaux sociaux pour suivre nos actualités. Facebook : https://www.facebook.com/InstitutHenriPoincare/ Twitter : https://tw
From playlist BOURBAKI - 2017
Bourbaki - 21/03/15 - 2/3 - Sophie GRIVAUX
Espaces de Banach possédant très peu d'opérateurs [d'après S. Argyros et R. Haydon]
From playlist Bourbaki - 21 mars 2015
[BOURBAKI 2017] 21/10/2017 - 3/4 - Olivier GUICHARD
Groupes convexes-cocompacts en rang supérieur ---------------------------------- Vous pouvez nous rejoindre sur les réseaux sociaux pour suivre nos actualités. Facebook : https://www.facebook.com/InstitutHenriPoincare/ Twitter : https://twitter.com/InHenriPoincare Instagram : https://www
From playlist BOURBAKI - 2017
(PP 6.2) Multivariate Gaussian - examples and independence
Degenerate multivariate Gaussians. Some sketches of examples and non-examples of Gaussians. The components of a Gaussian are independent if and only if they are uncorrelated.
From playlist Probability Theory
I. Gentil - Le problème de Schrödinger, un point de vue analytique (Part 3)
Ce cours est divisé en trois parties, le but étant de comprendre le problème de Schrödinger avec un point de vue analytique. Le premier cours porte sur le problème de Schrödinger. C’est un problème de minimisation de l’entropie sur un ensemble de mesures de probabilités sur les t
From playlist Rencontres du GDR AFHP 2019
Bernadette Perrin Riou - Promenade dans le jardin des symboles modulaires.
Je revisiterai un certain nombre de notions ou de résultats sur les symboles modulaires de Pollack-Stevens, le produit de Petersson ou les séries d'Eisenstein qui nous ont été utiles pour mettre en place dans Pari/GP les fonctions L p-adiques associées à des formes modulaires pour T0(N), l
From playlist The Paris-London Number Theory Seminar, Oct. 2019
Bourbaki - 21/03/15 - 1/3 - Sébastien GOUËZEL
Spectre du flot géodésique en courbure négative [d'après F. Faure et M. Tsuji]
From playlist Bourbaki - 21 mars 2015
[BOURBAKI 2017] 14/01/2017 - 1/4 - Cédric VILLANI
Inégalités isopérimétriques dans les espaces métriques mesurés, d’après F. Cavalletti et A. Mondino La théorie synthétique de la courbure de Ricci dans les espaces métriques mesurés a remporté ses premiers succès il y a une dizaine d’années, et s’est rapidement développée depuis ; elle ac
From playlist BOURBAKI - 2017
Ivan Gentil - Inégalités fonctionnelles et applications (Part 5)
Inégalités fonctionnelles et applications (Part 5)
From playlist Inter’actions en mathématiques 2015
A central limit theorem for Gaussian polynomials...... pt2 - Anindya De
Anindya De Institute for Advanced Study; Member, School of Mathematics May 13, 2014 A central limit theorem for Gaussian polynomials and deterministic approximate counting for polynomial threshold functions In this talk, we will continue, the proof of the Central Limit theorem from my las
From playlist Mathematics
G. Courtois - Compactness and Finiteness Results for Gromov-Hyperbolic Spaces 3 (version temporaire)
This is a series of lectures on Bishop--Gromov's type inequalities adapted to metric spaces. We consider the case of Gromov-hyperbolic spaces and draw consequences of these inequalities such as compactness and finiteness Theorems. This course is intended to be elementary in the sense that
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
Gaussian Integral 8 Original Way
Welcome to the awesome 12-part series on the Gaussian integral. In this series of videos, I calculate the Gaussian integral in 12 different ways. Which method is the best? Watch and find out! In this video, I present the classical way using polar coordinates, the one that Laplace original
From playlist Gaussian Integral
(PP 6.1) Multivariate Gaussian - definition
Introduction to the multivariate Gaussian (or multivariate Normal) distribution.
From playlist Probability Theory
[BOURBAKI 2019] Un lemme de fermeture C∞ - Humilière - 16/10/2019
Humilière () / 16.11.2019 Un lemme de fermeture C∞ Nous présenterons le contexte ainsi que certaines des idées menant à la démonstration par Asaoka et Irie du résultat suivant: C∞-génériquement, les orbites périodiques d'un difféomorphisme hamiltonien d'une surface compacte sont dense
From playlist BOURBAKI - 2019