Exotic probabilities | Continuous distributions
The Wigner quasiprobability distribution (also called the Wigner function or the Wigner–Ville distribution, after Eugene Wigner and Jean-André Ville) is a quasiprobability distribution. It was introduced by Eugene Wigner in 1932 to study quantum corrections to classical statistical mechanics. The goal was to link the wavefunction that appears in Schrödinger's equation to a probability distribution in phase space. It is a generating function for all spatial autocorrelation functions of a given quantum-mechanical wavefunction ψ(x).Thus, it maps on the quantum density matrix in the map between real phase-space functions and Hermitian operators introduced by Hermann Weyl in 1927, in a context related to representation theory in mathematics (see Weyl quantization). In effect, it is the Wigner–Weyl transform of the density matrix, so the realization of that operator in phase space. It was later rederived by Jean Ville in 1948 as a quadratic (in signal) representation of the local time-frequency energy of a signal, effectively a spectrogram. In 1949, José Enrique Moyal, who had derived it independently, recognized it as the quantum moment-generating functional, and thus as the basis of an elegant encoding of all quantum expectation values, and hence quantum mechanics, in phase space (see Phase-space formulation). It has applications in statistical mechanics, quantum chemistry, quantum optics, classical optics and signal analysis in diverse fields, such as electrical engineering, seismology, time–frequency analysis for music signals, spectrograms in biology and speech processing, and engine design. (Wikipedia).
Characteristic Polynomials of the Hermitian Wigner and Sample Covariance Matrices - Shcherbina
Tatyana Shcherbina Institute for Low Temperature Physics, Kharkov November 1, 2011 We consider asymptotics of the correlation functions of characteristic polynomials of the hermitian Wigner matrices Hn=n−1/2WnHn=n−1/2Wn and the hermitian sample covariance matrices Xn=n−1A∗m,nAm,nXn=n−1Am,n
From playlist Mathematics
(ML 7.7.A1) Dirichlet distribution
Definition of the Dirichlet distribution, what it looks like, intuition for what the parameters control, and some statistics: mean, mode, and variance.
From playlist Machine Learning
Keldysh Field Theory for Open Quantum Systems: Localization and Quantum Effects by Rajdeep Sensarma
Open Quantum Systems DATE: 17 July 2017 to 04 August 2017 VENUE: Ramanujan Lecture Hall, ICTS Bangalore There have been major recent breakthroughs, both experimental and theoretical, in the field of Open Quantum Systems. The aim of this program is to bring together leaders in the Open Q
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Multivariate Gaussian distributions
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Statistics: Ch 7 Sample Variability (3 of 14) The Inference of the Sample Distribution
Visit http://ilectureonline.com for more math and science lectures! To donate: http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will learn if the number of samples is greater than or equal to 25 then: 1) the distribution of the sample means is a normal distr
From playlist STATISTICS CH 7 SAMPLE VARIABILILTY
Likelihood | Log likelihood | Sufficiency | Multiple parameters
See all my videos here: http://www.zstatistics.com/ *************************************************************** 0:00 Introduction 2:17 Example 1 (Discrete distribution: develop your intuition!) 7:25 Likelihood 8:52 Likelihood ratio 10:00 Likelihood function 11:05 Log likelihood funct
From playlist Statistical Inference (7 videos)
Hypergeometric Distribution EXPLAINED!
See all my videos here: http://www.zstatistics.com/videos/ 0:00 Introduction 1:02 Quick Rundown 2:57 Probability Mass Function calculation 5:22 Cumulative Distribution Function calculation 6:48 Problem Question! Puck's flush: 0.0197
From playlist Distributions (10 videos)
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From playlist The Normal Distribution
Benson Au: "Finite-rank perturbations of random band matrices via infinitesimal free probability"
Asymptotic Algebraic Combinatorics 2020 "Finite-rank perturbations of random band matrices via infinitesimal free probability" Benson Au - University of California, San Diego (UCSD) Abstract: Free probability provides a unifying framework for studying random multi-matrix models in the la
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What is a Unimodal Distribution?
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From playlist Probability Distributions
Dyson Brownian motion, free fermions and connections to Random Matrix Theory by Gregory Schehr
PROGRAM : BANGALORE SCHOOL ON STATISTICAL PHYSICS - XII (ONLINE) ORGANIZERS : Abhishek Dhar (ICTS-TIFR, Bengaluru) and Sanjib Sabhapandit (RRI, Bengaluru) DATE : 28 June 2021 to 09 July 2021 VENUE : Online Due to the ongoing COVID-19 pandemic, the school will be conducted through online
From playlist Bangalore School on Statistical Physics - XII (ONLINE) 2021
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From playlist Physics of The Early Universe - An Online Precursor
Dyson Brownian motion, free fermions and connections to Random Matrix Theory-2 by Gregory Schehr
PROGRAM : BANGALORE SCHOOL ON STATISTICAL PHYSICS - XII (ONLINE) ORGANIZERS : Abhishek Dhar (ICTS-TIFR, Bengaluru) and Sanjib Sabhapandit (RRI, Bengaluru) DATE : 28 June 2021 to 09 July 2021 VENUE : Online Due to the ongoing COVID-19 pandemic, the school will be conducted through online
From playlist Bangalore School on Statistical Physics - XII (ONLINE) 2021
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ORGANIZERS: Abhishek Dhar and Sanjib Sabhapandit DATE: 27 June 2018 to 13 July 2018 VENUE: Ramanujan Lecture Hall, ICTS Bangalore This advanced level school is the ninth in the series. This is a pedagogical school, aimed at bridging the gap between masters-level courses and topics in
From playlist Bangalore School on Statistical Physics - IX (2018)
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From playlist Correlation and Disorder in Classical and Quantum Systems
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From playlist Bangalore School on Statistical Physics - X (2019)
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From playlist Applied Statistics (Entire Course)
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ORGANIZERS: Abhishek Dhar and Sanjib Sabhapandit DATE: 27 June 2018 to 13 July 2018 VENUE: Ramanujan Lecture Hall, ICTS Bangalore This advanced level school is the ninth in the series. This is a pedagogical school, aimed at bridging the gap between masters-level courses and topics in
From playlist Bangalore School on Statistical Physics - IX (2018)
OCR MEI Statistics Minor J: Poisson Distribution: 12 Approximating a Binomial
https://www.buymeacoffee.com/TLMaths Navigate all of my videos at https://sites.google.com/site/tlmaths314/ Like my Facebook Page: https://www.facebook.com/TLMaths-1943955188961592/ to keep updated Follow me on Instagram here: https://www.instagram.com/tlmaths/ Many, MANY thanks to Dea
From playlist OCR MEI Statistics Minor J: Poisson Distribution
Wigner Distribution Function and Integral Imaging | MIT 2.71 Optics, Spring 2009
Wigner Distribution Function and Integral Imaging Instructor: Michael McCanna, Michelle Lydia Kam Ye-Sien, Lei Tian, SHalin Mehta View the complete course: http://ocw.mit.edu/2-71S09 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at
From playlist MIT 2.71 Optics, Spring 2009