Category Archives: Probability

Test your intuition 43: Distribution According to Areas in Top Departments.

  In the community of mamathetitians in a certain country there are mamathetitians in two areas: Anabra (fraction p of the mamathetitians) and Algasis (fraction 1-p of  mamathetitians.) There are ten universities with 50 faculty members in each mamathetics department … Continue reading

Posted in Combinatorics, Open problems, Probability, Test your intuition | Tagged | 9 Comments

TYI 41: How many steps does it take for a simple random walk on the discrete cube to reach the uniform distribution?

Aeiel Yadin’s homepage contains great lecture notes on harmonic functions on groups and on various other topics. I have a lot of things to discuss and to report; exciting developments in the analysis of Boolean functions; much to report on … Continue reading

Posted in Combinatorics, Probability, Test your intuition | Tagged , , | Leave a comment

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 , , , | 4 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 , , | 2 Comments

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