Category Archives: Probability

Amazing! Keith Frankston, Jeff Kahn, Bhargav Narayanan, Jinyoung Park: Thresholds versus fractional expectation-thresholds

This post describes a totally unexpected breakthrough about expectation and thresholds. The result  by Frankston, Kahn, Narayanan, and Park has many startling applications and it builds on the recent breakthrough work of Alweiss, Lovett, Wu and Zhang on the sunflower … Continue reading

Posted in Combinatorics, Probability | Tagged , , , | 3 Comments

The story of Poincaré and his friend the baker

Update: After the embargo update (Oct 25): Now that I have some answers from the people involved let me make a quick update: 1) I still find the paper unconvincing, specifically, the few verifiable experiments (namely experiments that can be … Continue reading

Posted in Combinatorics, Computer Science and Optimization, Probability, Quantum, Statistics | Tagged , , | 24 Comments

Alef’s corner: Bicycles and the Art of Planar Random Maps

The artist behind Alef’s corner has a few mathematical designs and here are two new ones. (See Alef’s  website offering over 100 T-shirt designs.)   which was used for the official T-shirt for Jean-François Le Gall’s birthday conference. See also … Continue reading

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

Matan Harel, Frank Mousset, and Wojciech Samotij and the “the infamous upper tail” problem

Let me report today on a major breakthrough in random graph theory and probabilistic combinatorics. Congratulations to Matan, Frank, and Vojtek! Artist: Heidi Buck. “Catch a Dragon by the Tail 2” ( source ) Upper tails via high moments and entropic … Continue reading

Posted in Combinatorics, Probability | Tagged , , | 1 Comment

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 has been available for some time. (This proceedings’ 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 , , | 1 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 , | 4 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 | 1 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 , , , | 3 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