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 , , | Leave a comment

Imre Bárány: Limit shape

Limit shapes are fascinating objects in the interface between probability and geometry and between the discrete and the continuous. This post is kindly contributed by Imre Bárány. What is a limit shape? There are finitely many convex lattice polygons contained … Continue reading

Posted in Combinatorics, Convexity, Geometry, Guest blogger, Probability | Tagged , | 2 Comments

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 , , | 1 Comment

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 | Leave a comment

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 , , , | 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

Posted in Probability, Test your intuition | Tagged , | 8 Comments

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

Posted in Combinatorics, Probability | Tagged | 2 Comments

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 , , , , | Leave a comment

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 , , | 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

Posted in Combinatorics, Probability | Tagged , | Leave a comment