kazekkurz on More around Borsuk Gil Kalai on More around Borsuk kazekkurz on More around Borsuk Gil Kalai on Polymath 8 – a Succ… Patrick Poirier on About Alon Amit on NatiFest is Coming Abdulrahman Oladiipu… on The Kadison-Singer Conjecture… More around Borsuk |… on Helly’s Theorem, “… Gil Kalai on Polymath 8 – a Succ… Gil Kalai on Greg Kuperberg: It is in NP to… dmoskovich on Greg Kuperberg: It is in NP to… zhang twin prime bre… on Polymath 8 – a Succ…
- Many triangulated three-spheres!
- NatiFest is Coming
- More around Borsuk
- Analysis of Boolean Functions – Week 7
- Analysis of Boolean Functions week 5 and 6
- Real Analysis Introductory Mini-courses at Simons Institute
- Analysis of Boolean Functions – week 4
- Polymath 8 – a Success!
- Analysis of Boolean Functions – Week 3
Top Posts & Pages
- NatiFest is Coming
- Polymath 8 - a Success!
- Analysis of Boolean Functions
- The Kadison-Singer Conjecture has beed Proved by Adam Marcus, Dan Spielman, and Nikhil Srivastava
- Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
- Believing that the Earth is Round When it Matters
- 'Gina Says'
- Auction-based Tic Tac Toe: Solution
- Why is Mathematics Possible: Tim Gowers's Take on the Matter
Category Archives: Probability
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
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
We are considering the stable marriage theorem. Suppose that there are n men and n women. If the preferences are random and men are proposing, what is the likely average women’s rank of their husbands, and what is the likely average … Continue reading