In algebra and number theory, a distribution is a function on a system of finite sets into an abelian group which is analogous to an integral: it is thus the algebraic analogue of a distribution in the sense of generalised function. The original examples of distributions occur, unnamed, as functions φ on Q/Z satisfying Such distributions are called ordinary distributions. They also occur in p-adic integration theory in Iwasawa theory. Let ... → Xn+1 → Xn → ... be a projective system of finite sets with surjections, indexed by the natural numbers, and let X be their projective limit. We give each Xn the discrete topology, so that X is compact. Let φ = (φn) be a family of functions on Xn taking values in an abelian group V and compatible with the projective system: for some weight function w. The family φ is then a distribution on the projective system X. A function f on X is "locally constant", or a "step function" if it factors through some Xn. We can define an integral of a step function against φ as The definition extends to more general projective systems, such as those indexed by the positive integers ordered by divisibility. As an important special case consider the projective system Z/nZ indexed by positive integers ordered by divisibility. We identify this with the system (1/n)Z/Z with limit Q/Z. For x in R we let ⟨x⟩ denote the fractional part of x normalised to 0 ≤ ⟨x⟩ < 1, and let {x} denote the fractional part normalised to 0 < {x} ≤ 1. (Wikipedia).
(PP 6.1) Multivariate Gaussian - definition
Introduction to the multivariate Gaussian (or multivariate Normal) distribution.
From playlist Probability Theory
(PP 6.4) Density for a multivariate Gaussian - definition and intuition
The density of a (multivariate) non-degenerate Gaussian. Suggestions for how to remember the formula. Mathematical intuition for how to think about the formula.
From playlist Probability Theory
What is a Sampling Distribution?
Intro to sampling distributions. What is a sampling distribution? What is the mean of the sampling distribution of the mean? Check out my e-book, Sampling in Statistics, which covers everything you need to know to find samples with more than 20 different techniques: https://prof-essa.creat
From playlist Probability Distributions
Network Analysis. Lecture 2. Power laws.
Power law distribution. Scale-free networks.Pareto distribution, normalization, moments. Zipf law. Rank-frequency plot. Lecture slides: http://www.leonidzhukov.net/hse/2015/networks/lectures/lecture2.pdf
From playlist Structural Analysis and Visualization of Networks.
Distributions - Statistical Inference
In this video I talk about distribution, how to visualize it and also provide a concrete definition for it.
From playlist Statistical Inference
(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
Statistics: Introduction to the Shape of a Distribution of a Variable
This video introduces some of the more common shapes of distributions http://mathispower4u.com
From playlist Statistics: Describing Data
(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
The Normal Distribution (1 of 3: Introductory definition)
More resources available at www.misterwootube.com
From playlist The Normal Distribution
Nina Snaith - Combining random matrix theory and number theory [2015]
Name: Nina Snaith Event: Program: Foundations and Applications of Random Matrix Theory in Mathematics and Physics Event URL: view webpage Title: Combining random matrix theory and number theory Date: 2015-10-14 @11:00 AM Location: 313 Abstract: Many years have passed since the initial su
From playlist Number Theory
Law of large number & central limit theorem under uncertainty...
Law of large number & central limit theorem under uncertainty, the related new Ito's calculus and applications to risk measures, Shige Peng (Shandong University). Plenary Lecture from the 1st PRIMA Congress, 2009. Plenary Lecture 10. Abstract: You can view the abstract for this talk here:
From playlist PRIMA2009
CTNT 2022 - p-adic Fourier theory and applications (by Jeremy Teitelbaum)
This video is one of the special guess talks or conference talks that took place during CTNT 2022, the Connecticut Summer School and Conference in Number Theory. Note: not every special guest lecture or conference lecture was recorded. More about CTNT: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2022 - Conference lectures and special guest lectures
Random Matrices in Unexpected Places: Atomic Nuclei, Chaotic Billiards, Riemann Zeta #SoME2
Chapters: 0:00 Intro 2:21 What is RMT 7:12 Ensemble Averaging/Quantities of Interest 13:30 Gaussian Ensemble 18:03 Eigenvalues Repel 28:08 Recap 29:08 Three Surprising Coincidences 32:44 Billiards/Quantum Systems 36:00 Reimann Zeta ~~~~~~~~~~~~~~~~~~~~~~~~~ Errata + Clarifications ~~~~
From playlist Summer of Math Exposition 2 videos
Random Matrix Theory And its Applications by Satya Majumdar ( Lecture - 1 )
PROGRAM BANGALORE SCHOOL ON STATISTICAL PHYSICS - X ORGANIZERS : Abhishek Dhar and Sanjib Sabhapandit DATE : 17 June 2019 to 28 June 2019 VENUE : Ramanujan Lecture Hall, ICTS Bangalore This advanced level school is the tenth in the series. This is a pedagogical school, aimed at bridgin
From playlist Bangalore School on Statistical Physics - X (2019)
The measurement problem and some mild solutions by Dustin Lazarovici (Lecture - 03)
21 November 2016 to 10 December 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Quantum Theory has passed all experimental tests, with impressive accuracy. It applies to light and matter from the smallest scales so far explored, up to the mesoscopic scale. It is also a necessary ingredie
From playlist Fundamental Problems of Quantum Physics
Phiala Shanahan: "Machine learning for lattice field theory"
Machine Learning for Physics and the Physics of Learning 2019 Workshop I: From Passive to Active: Generative and Reinforcement Learning with Physics "Machine learning for lattice field theory" Phiala Shanahan, Massachusetts Institute of Technology (MIT) Abstract: I will discuss opportuni
From playlist Machine Learning for Physics and the Physics of Learning 2019
Statistical mechanics of deep learning by Surya Ganguli
Statistical Physics Methods in Machine Learning DATE: 26 December 2017 to 30 December 2017 VENUE: Ramanujan Lecture Hall, ICTS, Bengaluru The theme of this Discussion Meeting is the analysis of distributed/networked algorithms in machine learning and theoretical computer science in the
From playlist Statistical Physics Methods in Machine Learning
Benjamin Guedj: On generalisation and learning
A (condensed) primer on PAC-Bayes, followed by News from the PAC-Bayes frontline. LMS Computer Science Colloquium 2021
From playlist LMS Computer Science Colloquium Nov 2021
On the possibility of an instance-based complexity theory - Boaz Barak
Computer Science/Discrete Mathematics Seminar I Topic: On the possibility of an instance-based complexity theory. Speaker: Boaz Barak Affiliation: Harvard University Date: April 15, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics