Functional analysis | Free probability theory | Free algebraic structures
In the mathematical theory of free probability, the notion of free independence was introduced by Dan Voiculescu. The definition of free independence is parallel to the classical definition of independence, except that the role of Cartesian products of measure spaces (corresponding to tensor products of their function algebras) is played by the notion of a free product of (non-commutative) probability spaces. In the context of Voiculescu's free probability theory, many classical-probability theorems or phenomena have free probability analogs: the same theorem or phenomenon holds (perhaps with slight modifications) if the classical notion of independence is replaced by free independence. Examples of this include: the free central limit theorem; notions of free convolution; existence of and so on. Let be a , i.e. a unital algebra over equipped with a unital linear functional . As an example, one could take, for a probability measure , Another example may be , the algebra of matrices with the functional given by the normalized trace . Even more generally, could be a von Neumann algebra and a state on . A final example is the group algebra of a (discrete) group with the functional given by the group trace . Let be a family of unital subalgebras of . Definition. The family is called freely independent if whenever , and . If , is a family of elements of (these can be thought of as random variables in ), they are called freely independent if the algebras generated by and are freely independent. (Wikipedia).
What Does "Freedom of Speech" Mean in the U.S.? | History
What is free speech? How does the freedom of speech factor in to the U.S. Constitution? What are limitations and protections of free speech in the U.S.? Subscribe for more HISTORY: http://histv.co/SubscribeHistoryYT Newsletter: https://www.history.com/newsletter Website - http://www.hist
From playlist Examine the Past | History
America the Story of Us: Declaration of Independence | History
The Declaration of Independence marks the first such document declaring the equality of men. Own America: The Story of Us on DVD or Blu-ray! http://www.shophistorystore.com/ HISTORY®, now reaching more than 98 million homes, is the leading destination for award-winning original series and
From playlist Presidential History
Freedom of Speech: Crash Course Government and Politics #25
Today, FINALLY, Craig is going to talk about Free Speech! Now, free speech is so important because it not only allows you to critique the government, but it also protects you from the government. But it's essential to remember that not ALL speech is protected equally under the First Amendm
From playlist U.S. Government and Politics
Two Kinds of Freedom: Negative vs Positive Freedom
Another re-upload from the previous channel that I put together awhile ago about Isaiah Berlin's famous distinction between the notion of positive versus negative liberty, and the related liberal conception of freedom. More Short Videos: https://www.youtube.com/playlist?list=PLhP9EhPApKE8
From playlist Social & Political Philosophy
The Fourth Amendment | National Constitution Center | Khan Academy
Keep going! Check out the next lesson and practice what you’re learning: https://www.khanacademy.org/humanities/us-government-and-civics/us-gov-civil-liberties-and-civil-rights/us-gov-balancing-individual-freedom-with-public-order-and-safety/v/the-eighth-amendment A deep dive into the Fou
From playlist The Constitution, Bill of Rights, and Landmark Supreme Court Cases
Daniel Dennett - What is Free Will?
Free will is a problem. If it seems obvious that you are perfectly free to choose and decide, then it seems perfectly clear that you do not understand the problem. Free will is a huge problem, because our sense of free will and the physical structure of the world contradict each other. Fo
From playlist Understanding Free Will - Closer To Truth - Core Topic
Free to Choose Part 5: Created Equal Featuring Milton Friedman
For more videos: Facebook: www.facebook.com/FreeToChooseNetwork Media Website: http://freetochoosemedia.org/index.php Twitter: https://twitter.com/FreeToChooseNet Company: http://freetochoosenetwork.org Shop: http://www.freetochoose.net Stream: http://freetochoose.tv
From playlist "Free to Choose" by Milton Friedman
You don't have free will, but don't worry.
In this video I explain why free will is incompatible with the currently known laws of nature and why the idea makes no sense anyway. However, you don't need free will to act responsibly and to live a happy life, and I will tell you why. Support me on Patreon: https://www.patreon.com/Sabi
From playlist Philosophy of Science
If Free Will Is Illusory, How Do We Explain Our Experience Of Free Will?
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From playlist Science Unplugged: Big Ideas
9. Independence, Basis, and Dimension
MIT 18.06 Linear Algebra, Spring 2005 Instructor: Gilbert Strang View the complete course: http://ocw.mit.edu/18-06S05 YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8 9. Independence, Basis, and Dimension License: Creative Commons BY-NC-SA More information at h
From playlist MIT 18.06 Linear Algebra, Spring 2005
Camille Male - Distributional symmetry of random matrices...
Camille Male - Distributional symmetry of random matrices and the non commutative notions of independence
From playlist Spectral properties of large random objects - Summer school 2017
Distributional symmetries and non commutative (...) - C. Male - Workshop 2 - CEB T3 2017
Camille Male / 26.10.17 Distributional symmetries and non commutative notions of independence The properties of the limiting non commutative distribution of random matrices can be usually understood thanks to the symmetry of the model, e.g. Voiculescu's asymptotic free independence occur
From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester
From playlist Contributed talks One World Symposium 2020
Jonathan Barmak: Star clusters in clique complexes and the Vietoris-Rips complex of planar sets
Abstract: The star cluster of a simplex in a simplicial complex K is the union of the stars of its vertices. When K is clique, star clusters are contractible. We will recall applications of this notion to the study of homotopy invariants of independence complexes of graphs. If X is a plan
From playlist Vietoris-Rips Seminar
Matrix liberation process - Y. Ueda - Workshop 2 - CEB T3 2017
Yoshimichi Ueda / 24.10.17 Matrix liberation process We introduce a natural random matrix counterpart of the so-called liberation process introduced by Voiculescu in the framework of free probability, and consider its possible LDP in the large N limit. ---------------------------------
From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester
Anupam Gupta: The Independent Set problem on Degree d Graphs
Anupam Gupta: The Independent Set problem on Degree d Graphs The independent set problem on graphs with maximum degree d is known to be Ω(d/log2 d) hard to approximate, assuming the unique games conjecture. However, the best approximation algorithm was worse by about an Ω(log d) factor. I
From playlist HIM Lectures 2015
Calculating dimension and basis of range and kernel
German version here: https://youtu.be/lBdwtUa_BGM Support the channel on Steady: https://steadyhq.com/en/brightsideofmaths Official supporters in this month: - Petar Djurkovic - Lukas Mührke Here, I explain the typical calculation scheme for getting dimension and basis for the image/ran
From playlist Linear algebra (English)
Making a Math Concept Map | Ex: Linear Independence
Making concept maps are incredibly important in learning mathematics, far better than just a long list of isolated examples. I look at a key concept in Linear Algebra - Linear Independence - and make my own little concept map about it. You can be creative when you make your own, this is ju
From playlist Learning Math Advice
Eigenvalue bounds on sums of random matrices - Adam Marcus
Members’ Seminar Topic:Eigenvalue bounds on sums of random matrices Speaker: Adam Marcus Affilation: Princeton University Date: November 14, 2016 For more videos, visit http://video.ias.edu
From playlist Mathematics
The American Revolution: Crash Course Black American History #8
When we talk about the American Revolution and Revolutionary War, the discussion often involves lofty ideals like liberty, freedom, and justice. The Declaration of Independence even opens with the idea that "all men are created equal." But it turns out, the war wasn't being fought on behal
From playlist Black American History