Category Archives: Probability

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 | 25 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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Is Backgammon in P?

  The Complexity of Zero-Sum Stochastic Games with Perfect Information Is there a polynomial time algorithm for chess?  Well, if we consider the complexity of chess in terms of the board size then it is fair to think that the answer is … Continue reading

Posted in Computer Science and Optimization, Games, Open problems, Probability | 9 Comments

Emmanuel Abbe: Erdal Arıkan’s Polar Codes

Click here for the most recent polymath3 research thread. A new thread is comming soon.   Emmanuel Abbe and Erdal Arıkan This post is authored by Emmanuel Abbe A new class of codes, called polar codes, recently made a breakthrough … Continue reading

Posted in Information theory, Probability | Tagged , | 17 Comments

Benoît’s Fractals

Mandelbrot set Benoît Mandelbrot passed away a few dayes ago on October 14, 2010. Since 1987, Mandelbrot was a member of the Yale’s mathematics department. This chapterette from my book “Gina says: Adventures in the Blogosphere String War”   about fractals is brought here on this … Continue reading

Posted in Geometry, Obituary, Physics, Probability | 6 Comments

Midrasha Talks are Now Online

Itai Benjamini listening to Gadi Kozma There are 41 lectures from the Midrasha on Probability and Geometry: The Mathematics of Oded Schramm which are now online. Joram Lindenstrauss’s concluding lecture (click on the picture to see) Laci Lovasz More pictures … Continue reading

Posted in Combinatorics, Conferences, Probability | Tagged , , | 4 Comments

Test Your Intuition (11): Is it Rational to Insure a Toaster

Here is a question from last year’s exam in the course “Basic Ideas of Mathematics”:   You buy a toaster for 200 NIS ($50) and you are offered one year of insurance for 24 NIS ($6).   a) Is it … Continue reading

Posted in Probability, Rationality, Teaching, Test your intuition | Tagged , | 18 Comments

Itamar Pitowsky: Probability in Physics, Where does it Come From?

I came across a videotaped lecture by Itamar Pitowsky given at PITP some years ago on the question of probability in physics that we discussed in two earlier posts on randomness in nature (I, II). There are links below to … Continue reading

Posted in Obituary, Philosophy, Physics, Probability | Tagged , , , | 1 Comment