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Category Archives: Probability
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
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
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
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
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
Following are some preliminary observations connecting BosonSampling, an interesting computational task that quantum computers can perform (that we discussed in this post), and noise-sensitivity in the sense of Benjamini, Schramm, and myself (that we discussed here and here.) BosonSampling and computational-complexity hierarchy-collapse Suppose that … Continue reading
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 Kirchhoff and Wilson via Kozdron and Stroock. The lecture is based on … Continue reading
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
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