A random function – of either one variable (a random process), or two or more variables(a random field) – is called Gaussian if every finite-dimensional distribution is a multivariate normal distribution. Gaussian random fields on the sphere are useful (for example) when analysing * the anomalies in the cosmic microwave background radiation (see, pp. 8–9); * brain images obtained by positron emission tomography (see, pp. 9–10). Sometimes, a value of a Gaussian random function deviates from its expected value by several standard deviations. This is a large deviation. Though rare in a small domain (of space or/and time), large deviations may be quite usual in a large domain. (Wikipedia).
Multivariate Gaussian distributions
Properties of the multivariate Gaussian probability distribution
From playlist cs273a
In this video we discuss the Gaussian (AKA Normal) probability distribution function. We show how it relates to the error function (erf) and discuss how to use this distribution analytically and numerically (for example when analyzing real-life sensor data or performing simulation of stoc
From playlist Probability
Order Graphs of a Normal Distribution by Standard Deviation
This video explains how to order graph from least to greatest based up the standard deviation.
From playlist The Normal Distribution
How to find the number of standard deviations that it takes to represent all the data
👉 Learn how to find the variance and standard deviation of a set of data. The variance of a set of data is a measure of spread/variation which measures how far a set of numbers is spread out from their average value. The standard deviation of a set of data is a measure of spread/variation
From playlist Variance and Standard Deviation
From playlist Contributed talks One World Symposium 2020
Prob & Stats - Random Variable & Prob Distribution (30 of 53) Standard Deviation
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the standard deviation of random variables. Next video in series: http://youtu.be/XiTMW8-aXXM
From playlist iLecturesOnline: Probability & Stats 2: Random Variable & Probability Distribution
Top eigenvalue of a Gaussian random matrix: Large Deviations by Satya Majumdar
Large deviation theory in statistical physics: Recent advances and future challenges DATE: 14 August 2017 to 13 October 2017 VENUE: Madhava Lecture Hall, ICTS, Bengaluru Large deviation theory made its way into statistical physics as a mathematical framework for studying equilibrium syst
From playlist Large deviation theory in statistical physics: Recent advances and future challenges
A tale of two point processes in the plane by Manjunath Krishnapur
Large deviation theory in statistical physics: Recent advances and future challenges DATE: 14 August 2017 to 13 October 2017 VENUE: Madhava Lecture Hall, ICTS, Bengaluru Large deviation theory made its way into statistical physics as a mathematical framework for studying equilibrium syst
From playlist Large deviation theory in statistical physics: Recent advances and future challenges
Ofer Zeitouni: Large Deviations at Work
This lecture was held at The University of Oslo, May 24, 2007 and was part of the Abel Prize Lectures in connection with the Abel Prize Week celebrations. Program for the Abel Lectures 2007 1. “A Short History of Large Deviations” by Srinivasa Varadhan, Abel Laureate 2007, Courant I
From playlist Abel Lectures
Large deviations theory applied to large scale (...) - P. Reimberg - Workshop 1 - CEB T3 2018
Paulo Reimberg (IPhT) / 20.09.2018 Large deviations theory applied to large scale structure cosmology ---------------------------------- Vous pouvez nous rejoindre sur les réseaux sociaux pour suivre nos actualités. Facebook : https://www.facebook.com/InstitutHenriPoincare/ Twitter : ht
From playlist 2018 - T3 - Analytics, Inference, and Computation in Cosmology
Joscha Prochno: The large deviations approach to high-dimensional convex bodies, Lecture I
Given any isotropic convex body in high dimension, it is known that its typical random projections will be approximately standard Gaussian. The universality in this central limit perspective restricts the information that can be retrieved from the lower-dimensional projections. In contrast
From playlist Workshop: High dimensional spatial random systems
Joscha Prochno: The large deviations approach to high-dimensional convex bodies, lecture III
Given any isotropic convex body in high dimension, it is known that its typical random projections will be approximately standard Gaussian. The universality in this central limit perspective restricts the information that can be retrieved from the lower-dimensional projections. In contrast
From playlist Workshop: High dimensional spatial random systems
Joscha Prochno: The large deviations approach to high-dimensional convex bodies II
Given any isotropic convex body in high dimension, it is known that its typical random projections will be approximately standard Gaussian. The universality in this central limit perspective restricts the information that can be retrieved from the lower-dimensional projections. In contrast
From playlist Workshop: High dimensional spatial random systems
Ella Hiesmayr (UC Berkeley) -- Edge large deviations of sparse matrices with non-Gaussian weights
Large deviations of the spectral properties of random matrices have been an active area of research for several decades. These questions were first addressed for matrices with independent Gaussian entries relying on an analysis of the joint density of the eigenvalues available in this
From playlist Northeastern Probability Seminar 2021
(PP 6.10) Sum of independent Gaussians
A sum of independent (multivariate) Gaussians is (multivariate) Gaussian, with mean equal to the sum of the means, and covariance equal to the sum of the covariances.
From playlist Probability Theory
Top Eigenvalue of a Random Matrix: A tale of tails - Satya Majumdar
Speaker : Satya Majumdar (Directeur de Recherche in CNRS) Date and Time : 27 Jan 2012, 04:00 PM Venue : New Physical Sciences Building Auditorium, IISc, Bangalore Random matrices were first introduced by Wishart (1928) in the statistics literature to describe the covariance matrix of la
From playlist Top Eigenvalue of a Random Matrix: A tale of tails - Satya Majumdar
Large Deviations for the Largest Eigenvalue of Sub-Gaussian Wigner Matrices by Nicholas Cook
PROGRAM: TOPICS IN HIGH DIMENSIONAL PROBABILITY ORGANIZERS: Anirban Basak (ICTS-TIFR, India) and Riddhipratim Basu (ICTS-TIFR, India) DATE & TIME: 02 January 2023 to 13 January 2023 VENUE: Ramanujan Lecture Hall This program will focus on several interconnected themes in modern probab
From playlist TOPICS IN HIGH DIMENSIONAL PROBABILITY