Category Archives: Probability

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 , , , | 8 Comments

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 , , | 4 Comments

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

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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 , , | 14 Comments

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

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Itai Ashlagi, Yashodhan Kanoria, and Jacob Leshno: What a Difference an Additional Man makes?

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

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Test Your Intuition (19): The Advantage of the Proposers in the Stable Matching Algorithm

Stable mariage The Gale-Shapley stable matching theorem and the algorithm. GALE-SHAPLEY THEOREM Consider a society of n men and n women and suppose that every man [and every woman] have a preference (linear) relation on the women [men] he [she] knows. Then … Continue reading

Posted in Combinatorics, Games, Probability, Test your intuition | Tagged , , , , , , | 7 Comments

Test Your Intuition (18): How many balls will be left when only one color remains?

(Thanks to Itai Benjamini and Ronen Eldan.) Test (quickly) your intuition:  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 … Continue reading

Posted in Probability, Test your intuition | 26 Comments

What does “beyond a reasonable doubt” practically mean?

(Motivated by two questions from Gowers’s How should mathematics be taught to non mathematicians.)

Posted in Law, Probability, Test your intuition | 18 Comments

Noise Sensitivity and Percolation. Lecture Notes by Christophe Garban and Jeff Steif

Lectures on noise sensitivity and percolation is a new beautiful monograph by Christophe Garban and Jeff Steif. (Some related posts on this blog: 1, 2, 3, 4, 5)

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