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Category Archives: Probability
Influence, Threshold, and Noise
My dear friend Itai Benjamini told me that he won’t be able to make it to my Tuesday talk on influence, threshold, and noise, and asked if I already have the slides. So it occurred to me that perhaps … Continue reading
Analysis of Boolean Functions week 5 and 6
Lecture 7 First passage percolation 1) Models of percolation. We talked about percolation introduced by Broadbent and Hammersley in 1957. The basic model is a model of random subgraphs of a grid in n-dimensional space. (Other graphs were considered later as … Continue reading
Posted in Combinatorics, Computer Science and Optimization, Probability, Teaching
Tagged Arrow's theorem, Percolation
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Analysis of Boolean Functions – Week 3
Lecture 4 In the third week we moved directly to the course’s “punchline” – the use of Fourier-Walsh expansion of Boolean functions and the use of Hypercontractivity. Before that we started with a very nice discrete isoperimetric question on a … Continue reading
Analysis of Boolean functions – week 2
Post on week 1; home page of the course analysis of Boolean functions Lecture II: We discussed two important examples that were introduced by Ben-Or and Linial: Recursive majority and tribes. Recursive majority (RM): is a Boolean function with variables … Continue reading
Posted in Combinatorics, Computer Science and Optimization, Probability, Teaching
Tagged Boolean functions, Tribes
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Poznań: Random Structures and Algorithms 2013
Michal Karonski (left) who built Poland’s probabilistic combinatorics group at Poznań, and a sculpture honoring the Polish mathematicians who first broke the Enigma machine (right, with David Conlon, picture taken by Jacob Fox). I am visiting now Poznań for the 16th … Continue reading
Posted in Combinatorics, Conferences, Open problems, Philosophy, Probability
Tagged Poznan, RSA
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BosonSampling and (BKS) Noise Sensitivity
Update (Nov 2014): Noise sensitivity of BosonSampling and computational complexity of noisy BosonSampling are studied in this paper by Guy Kindler and me. Some of my predictions from this post turned out to be false. In particular the noisy BosonSampling … Continue reading
Posted in Computer Science and Optimization, Physics, Probability
Tagged BosonSampling, Noise, Noise-sensitivity, Quantum computation
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Lawler-Kozdron-Richards-Stroock’s combined Proof for the Matrix-Tree theorem and Wilson’s Theorem
David Wilson and a cover of Shlomo’s recent book “Curvature in mathematics and physics” A few weeks ago, in David Kazhdan’s basic notion seminar, Shlomo Sternberg gave a lovely presentation Kirchho ff and Wilson via Kozdron and Stroock. The lecture is based on … Continue reading
Posted in Combinatorics, Computer Science and Optimization, Probability
Tagged David Wilson, Gustav Kirchhoff, Trees
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Oz’ Balls Problem: The Solution
A commentator named Oz proposed the following question: You have a box with n red balls and n blue balls. You take out each time a ball at random but, if the ball was red, you put it back in the box and take out … Continue reading
Posted in Probability, Test your intuition
Tagged Erosion, J. F. C. Kingman, Probability, S. E. Volkov
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Taking balls away: Oz’ Version
This post is based on a comment by Oz to our question about balls with two colors: “There is an interesting (and more difficult) variation I once heard but can’t recall where: You have a box with n red balls … Continue reading
Posted in Guest post, Probability, Test your intuition
Tagged Oz, Probability, Test your intuition
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Answer to test your intuition (18)
You have a box with n red balls and n blue balls. You take out balls one by one at random until left only with balls of the same color. How many balls will be left (as a function of n)? … Continue reading
Posted in Probability, Test your intuition
Tagged Itai Benjamini, Probability, random permutation, Ronen Eldan, Test your intuition
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