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Category Archives: Probability
Itai Benjamini and Jeremie Brieussel: Noise Sensitivity Meets Group Theory
The final version of my ICM 2018 paper Three puzzles on mathematics computation and games is available for some time. (This proceeding’s version unlike the arXived version has a full list of references.) In this post I would like to … Continue reading
Posted in Algebra, Combinatorics, Probability
Tagged Itai Benjamini, Jeremie Brieussel, Noise-sensitivity
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Answer to TYI 37: Arithmetic Progressions in 3D Brownian Motion
Consider a Brownian motion in three dimensional space. We asked (TYI 37) What is the largest number of points on the path described by the motion which form an arithmetic progression? (Namely, , so that all are equal.) Here is … Continue reading
Posted in Combinatorics, Open discussion, Probability
Tagged Brownian motion, Gady Kozma, Itai Benjamini
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Gothenburg, Stockholm, Lancaster, Mitzpe Ramon, and Israeli Election Day 2019
Lancaster – Watching the outcomes of the Israeli elections (photo: Andrey Kupavskii) Sweden I just came back from a trip to Sweden and the U.K. I was invited to Gothenburg to be the opponent for a Ph. D. Candidate Malin … Continue reading
Posted in Combinatorics, Probability, Updates
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TYI38 Lior Kalai: Monty Hall Meets Survivor
For breaking news, scroll down. Lior Kalai: Survivor Meets the Monty Hall Puzzle We start with the classical question and go on with a new version contributed by my son Lior. Update: A few brief comments on the original problem … Continue reading
Posted in Probability, Riddles, Test your intuition
Tagged Karen Uhlenbeck, Lior Kalai, Monty Hall problem, Survivor
2 Comments
Test Your Intuition (or simply guess) 37: Arithmetic Progressions for Brownian Motion in Space
Consider a Brownian motion in three dimensional space. What is the largest number of points on the path described by the motion which form an arithmetic progression? (Namely, , so that all are equal.) A 2-D picture; In … Continue reading
Konstantin Tikhomirov: The Probability that a Bernoulli Matrix is Singular
Konstantin Tikhomirov An old problem in combinatorial random matrix theory is cracked! Singularity of random Bernoulli matrices by Konstantin Tikhomirov Abstract: For each , let be an n×n random matrix with independent ±1 entries. We show that P( is singular}=, … Continue reading
Exciting Beginning-of-the-Year Activities and Seminars.
Let me mention two talks with very promising news by friends of the blog, Karim Adiprasito and Noam Lifshitz. As always, with the beginning of the academic year there are a lot of exciting activities, things are rather hectic around, … Continue reading
Posted in Combinatorics, Geometry, Probability
Tagged Dor Minzer, Eoin Long, Karim Adiprasito, Noam Lifshitz, Peter Keevash
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Duncan Dauvergne and Bálint Virág Settled the Random Sorting Networks Conjectures
A short summary: The beautiful decade-old conjectures on random sorting networks by Omer Angel, Alexander Holroyd, Dan Romik, and Bálint Virág, have now been settled by Duncan Dauvergne and Bálint Virág in two papers: Circular support in random sorting networks, by Dauvergne … Continue reading
Posted in Combinatorics, Probability, Updates
Tagged Bálint Virág, Dubcan Dauvergne, Random sorting networks
2 Comments
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
