Probabilistic inequalities | Geometric inequalities | Gaussian function
The Gaussian correlation inequality (GCI), formerly known as the Gaussian correlation conjecture (GCC), is a mathematical theorem in the fields of mathematical statistics and convex geometry. A special case of the inequality was published as a conjecture in a paper from 1955; further development was given by Olive Jean Dunn in 1958. The general case was stated in 1972, also as a conjecture. The inequality remained unproven until 2014, when Thomas Royen, a retired German statistician, proved it using relatively elementary tools. The proof did not gain attention when it was published in 2014, due to Royen's relative anonymity and that the proof was published in a predatory journal. Another reason was a history of false proofs (by others) and many failed attempts to prove the conjecture, causing skepticism among mathematicians in the field. The conjecture, and its solution, came to public attention in 2017, when reports of Royen's proof were published in mainstream media. (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
Joe Neeman: Gaussian isoperimetry and related topics I
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
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
Joe Neeman: Gaussian isoperimetry and related topics III
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 6.1) Multivariate Gaussian - definition
Introduction to the multivariate Gaussian (or multivariate Normal) distribution.
From playlist Probability Theory
Multivariate Gaussian distributions
Properties of the multivariate Gaussian probability distribution
From playlist cs273a
(PP 6.6) Geometric intuition for the multivariate Gaussian (part 1)
How to visualize the effect of the eigenvalues (scaling), eigenvectors (rotation), and mean vector (shift) on the density of a multivariate Gaussian.
From playlist Probability Theory
This video explains how to find the correlation coefficient which describes the strength of the linear relationship between two variables x and y. My Website: https://www.video-tutor.net Patreon: https://www.patreon.com/MathScienceTutor Amazon Store: https://www.amazon.com/shop/theorga
From playlist Statistics
(PP 6.7) Geometric intuition for the multivariate Gaussian (part 2)
How to visualize the effect of the eigenvalues (scaling), eigenvectors (rotation), and mean vector (shift) on the density of a multivariate Gaussian.
From playlist Probability Theory
Workshop 1 "Operator Algebras and Quantum Information Theory" - CEB T3 2017 - I.Villanueva
Ignacio Villanueva (Madrid) / 11.09.17 Title: Random quantum correlations are generically non classical Abstract: Non-locality is certified by the existence of quantum bipartite correlations which are non-explainable by any classical model. Once we know the existence of these, we are fac
From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester
[BOURBAKI 2017] 14/01/2017 - 2/4 - Franck BARTHE
L’inégalité de corrélation gaussienne, d’après Thomas Royen La conjecture de corrélation gaussienne prédit que pour toute mesure gaussienne centrée et tout couple d’ensembles convexes symétriques par rapport à l’origine, la mesure de l’intersection des ensembles est plus grande que le pro
From playlist BOURBAKI - 2017
Marginal triviality of the scaling limits of critical 4D Ising (Lecture 3) by Hugo Duminil-Copin
INFOSYS-ICTS RAMANUJAN LECTURES CRITICAL PHENOMENA THROUGH THE LENS OF THE ISING MODEL SPEAKER: Hugo Duminil-Copin (Institut des Hautes Études Scientifiques, France & University of Geneva, Switzerland) DATE: 09 January 2023 to 13 January 2023 VENUE: Ramanujan Lecture Hall Lecture 1 D
From playlist Infosys-ICTS Ramanujan Lectures
Log-Sobolev inequality for near critical Ising and continuum φ4 measures - Roland Bauerschmidt
Mathematical Physics Seminar Topic: Log-Sobolev inequality for near critical Ising and continuum φ4 measures Speaker: Roland Bauerschmidt Affiliation: University of Cambridge Date: February 23, 2022 I will present results on Glauber dynamics of Ising models and continuum φ4 measures.
From playlist Mathematics
Hugo Duminil-Copin: Lecture #1
First lecture on "Marginal triviality of the scaling limits of critical 4D Ising and ϕ^4_4 models" by Professor Hugo Duminil-Copin. Unfortunately due to the technical difficulties (read organisers did not start the recording on time) first 10 minutes of the lecture are missing. These 10 m
From playlist Summer School on PDE & Randomness
Roland Bauerschmidt - Perspectives on the renormalisation group approach
The goal of this talk is to review some of the successes but also the outstanding challenges of the renormalisation group approach to the Ising and \varphi^4 models. I will also try to describe a common perspective of the usual approach to the renormalisation group based on perturbation th
From playlist 100…(102!) Years of the Ising Model
Thomas Courtade : Information Theoretic Perspective on Brascamp -Lieb- Barthe Inequalities
Recording during the thematic meeting : "Geometrical and Topological Structures of Information" the August 28, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent
From playlist Geometry
Nexus Trimester - Thomas Courtade (UC-Berkeley)
Strong Data Processing and the Entropy Power Inequality Thomas Courtade (UC-Berkeley) February 10, 2016 Abstract: Proving an impossibility result in information theory typically boils down to quantifying a tension between information measures that naturally emerge in an operational setti
From playlist Nexus Trimester - 2016 - Distributed Computation and Communication Theme
(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
Marginal triviality of the scaling limits of critical 4D Ising (Lecture 4) by Hugo Duminil-Copin
INFOSYS-ICTS RAMANUJAN LECTURES CRITICAL PHENOMENA THROUGH THE LENS OF THE ISING MODEL SPEAKER: Hugo Duminil-Copin (Institut des Hautes Études Scientifiques, France & University of Geneva, Switzerland) DATE: 09 January 2023 to 13 January 2023 VENUE: Ramanujan Lecture Hall Lecture 1 D
From playlist Infosys-ICTS Ramanujan Lectures