Category Archives: Probability

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

Posted in Combinatorics, Probability, Test your intuition | Tagged | 36 Comments

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

Posted in Combinatorics, Probability, Test your intuition | Tagged | 21 Comments

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

Two Delightful Major Simplifications

Arguably mathematics is getting harder, although some people claim that also in the old times parts of it were hard and known only to a few experts before major simplifications had changed  matters. Let me report here about two recent remarkable simplifications … Continue reading

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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

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