Category Archives: Probability

Itai Benjamini: Coarse Uniformization and Percolation & A Paper by Itai and me in Honor of Lucio Russo

Here is another video of a smashing short talk by my dear friend Itai Benjamini with beautiful conjectures proposing an important new step in the connection between percolation and conformal geometry. Here is the link to Itai’s original paper Percolation … Continue reading

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Bálint Virág: Random matrices for Russ

You can watch now all the videos for Russfest Elegance in Probability. Many great talks! I just watched Bálint Virág‘s lecture “Random matrices for Russ”. Highly recommended.

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TYI 31 – Rados Radoicic’s Rope Problem

  Ropemaker (source) Rados Radoicic wrote me: “Several years back, I heard the following puzzle that turns out to be rather ‘classical’: “There are N ropes in a bag. In each step, two rope ends are picked uniformly at random, tied … Continue reading

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Elchanan Mossel’s Amazing Dice Paradox (your answers to TYI 30)

TYI 30 asked Elchanan Mossel’s Amazing Dice Paradox (that I heard from Yuval Peres yesterday) You throw a die until you get 6. What is the expected number of throws (including the throw giving 6) conditioned on the event that all throws … Continue reading

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TYI 30: Expected number of Dice throws

Test your intuition: You throw a dice until you get 6. What is the expected number of throws (including the throw giving 6) conditioned on the event that all throws gave even numbers. follow-up post

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Test your intuition 29: Diameter of various random trees

Both trees in general and random trees in particular are wonderful objects. And there is nothing more appropriate to celebrate Russ Lyons great birthday conference “Elegance in Probability” (taking place now in Tel Aviv) than to test your intuition, dear … Continue reading

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Boolean Functions: Influence, Threshold, and Noise

Here is the written version of my address at the 7ECM last July in Berlin. Boolean functions, Influence, threshold, and Noise Trying to follow an example of a 1925 lecture by Landau (mentioned in the lecture), the writing style is very … Continue reading

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The US Elections and Nate Silver: Informtion Aggregation, Noise Sensitivity, HEX, and Quantum Elections.

Being again near general  elections is  an opportunity to look at some topics we talked about over the years. I am quite fond of (and a bit addicted to) Nate Silver’s site FiveThirtyEight. Silver’s models tell us what is the probability that … Continue reading

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TYI 26: Attaining the Maximum

(Thanks, Dani!) Given a random sequence , ******, , let . and assume that .  What is the probability that the maximum value of is attained only for a single value of ? Test your intuition: is this probability bounded … Continue reading

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More Reasons for Small Influence

Readers of the big-league ToC blogs have already heard about the breakthrough paper An average-case depth hierarchy theorem for Boolean circuits by Benjamin Rossman, Rocco Servedio, and Li-Yang Tan. Here are blog reports on Computational complexity, on the Shtetl Optimized, and of Godel … Continue reading

Posted in Combinatorics, Computer Science and Optimization, Open problems, Probability | 12 Comments