In probability theory, Gauss's inequality (or the Gauss inequality) gives an upper bound on the probability that a unimodal random variable lies more than any given distance from its mode. Let X be a unimodal random variable with mode m, and let τ 2 be the expected value of (X − m)2. (τ 2 can also be expressed as (μ − m)2 + σ 2, where μ and σ are the mean and standard deviation of X.) Then for any positive value of k, The theorem was first proved by Carl Friedrich Gauss in 1823. (Wikipedia).
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 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 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
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
(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
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
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
PUSHING A GAUSSIAN TO THE LIMIT
Integrating a gaussian is everyones favorite party trick. But it can be used to describe something else. Link to gaussian integral: https://www.youtube.com/watch?v=mcar5MDMd_A Link to my Skype Tutoring site: dotsontutoring.simplybook.me or email dotsontutoring@gmail.com if you have ques
From playlist Math/Derivation Videos
Emanuel Milman - The log-Minkowski Problem - IPAM at UCLA
Recorded 09 February 2022. Emanuel Milman of Technion - Israel Institute of Technology presents "The log-Minkowski Problem" at IPAM's Calculus of Variations in Probability and Geometry Workshop. Abstract: The classical Minkowski problem asks to find a convex body K in Rn having a prescrib
From playlist Workshop: Calculus of Variations in Probability and Geometry
Gaussian Brunn-Minkowski Theory by Mokshay Madiman
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
Zero mean curvature surfaces in Euclidean and Lorentz-Minkowski....(Lecture 1) by Shoichi Fujimori
Discussion Meeting Discussion meeting on zero mean curvature surfaces (ONLINE) Organizers: C. S. Aravinda and Rukmini Dey Date: 07 July 2020 to 15 July 2020 Venue: Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the meeting will be conduct
From playlist Discussion Meeting on Zero Mean Curvature Surfaces (Online)
Frank Morgan: Isoperimetry with density
Abstract : In 2015 Chambers proved the Log-convex Density Conjecture, which says that for a radial density f on Rn, spheres about the origin are isoperimetric if and only if log f is convex (the stability condition). We discuss recent progress and open questions for other densities, unequa
From playlist Control Theory and Optimization
8ECM Plenary Lecture: Franc Forstnerič
From playlist 8ECM Plenary Lectures
Quadratic Reciprocity proof -- Number Theory 23
Suggest a problem: https://forms.gle/ea7Pw7HcKePGB4my5 Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Patreon: https://www.patreon.com/michaelpennmath Merch: https://teespring.com/stores/michael-penn-math Personal Website: http://www.michael-penn.net Randolp
From playlist Number Theory v2
Proving Quadratic Reciprocity — Number Theory 23
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From playlist Number Theory
Mod-01 Lec-25 Effect of Small Pivots
Elementary Numerical Analysis by Prof. Rekha P. Kulkarni,Department of Mathematics,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in
From playlist NPTEL: Elementary Numerical Analysis | CosmoLearning Mathematics
Physics - E&M: Maxwell's Equations (9 of 30) Differential Form of Gauss' Law: 1
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain Gauss' Law in differential form.
From playlist PHYSICS 46 MAXWELL'S EQUATIONS
Skewes' Massive Number - Numberphile
Dr James Grime on the epic Skewes' Number. Lynda free trial (worth a look): http://www.lynda.com/numberphile More links & stuff in full description below ↓↓↓ Prime numbers: http://bit.ly/primevids Graham's Number: http://bit.ly/GrahamsNumber A small bit we chopped from this video: https:
From playlist Big Numbers on Numberphile