Category Archives: Probability

Bo’az Klartag and Joseph Lehec: The Slice Conjecture Up to Polylogarithmic Factor!

Bo’az Klartag (right) and Joseph Lehec (left) In December 2020, we reported on Yuansi Chen breakthrough result on Bourgain’s alicing problem and the Kannan Lovasz Simonovits conjecture. It is a pleasure to report on a further fantastic progress on these … Continue reading

Posted in Analysis, Computer Science and Optimization, Convexity, Geometry, Probability | Tagged , | 3 Comments

Test Your intuition 51

Suppose that and are two compact convex sets in space. Suppose that contains . Now consider two quantities is the average volume of a simplex forms by four points in drawn uniformly at random. is the average volume of a … Continue reading

Posted in Convexity, Geometry, Probability, Test your intuition | Tagged | 12 Comments

Answer to Test Your Intuition 50: Detecting a Deviator

Two weeks ago we asked: Ruth and Ron start together at the origin and take a walk on the integers. Every day they make a move. They take turns in flipping a coin and they move together right or left … Continue reading

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

Test Your Intuition 50. Two-Player Random Walk; Can You Detect Who Did Not Follow the Rules?

Ruth and Ron start together at the origin and take a walk on the integers. Every day they make a move. They take turns in flipping a coin and they move together right or left according to the outcome. Their … Continue reading

Posted in Probability, Test your intuition | Tagged , | 13 Comments

ICM 2022 awarding ceremonies (1)

Hugo Duminil-Copin, June Huh, James Maynard and Maryna Viazovska were awarded the Fields Medal 2022 and Mark Braverman was awarded the Abacus Medal 2022. I am writing from Helsinki where I attended the meeting of the General Assembly of the … Continue reading

Posted in Academics, Algebra, Applied mathematics, Combinatorics, Computer Science and Optimization, Convexity, Geometry, ICM2022, Probability | 7 Comments

Amazing: Jinyoung Park and Huy Tuan Pham settled the expectation threshold conjecture!

A brief summary: In the paper, A proof of the Kahn-Kalai conjecture, Jinyoung Park and Huy Tuan Pham proved the 2006 expectation threshold conjecture posed by Jeff Kahn and me. The proof is wonderful. Congratulations Jinyoung and Huy Tuan! Updates: … Continue reading

Posted in Combinatorics, Probability | Tagged , | 9 Comments

Face to face talks and recorded videotaped introductions

Many face to face activities are now resuming. Last week I took part in a great conference on high dimensional expanders at the Simons Foundation, I recently gave real life talks with large audiences also in U. Chicago and Rutgers, … Continue reading

Posted in Combinatorics, Physics, Probability, Quantum, Updates | Leave a comment

To cheer you up in difficult times 32, Annika Heckel’s guest post: How does the Chromatic Number of a Random Graph Vary?

This is a guest post kindly written by Annika Heckel. We first reported about Annika Heckel’s breakthrough in this post. A pdf version of this post can be found here. Pick an -vertex graph uniformly at random. Pick another one. … Continue reading

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

The Argument Against Quantum Computers – A Very Short Introduction

Left: Gowers’s book Mathematics a very short introduction. Right C. elegans; Boson Sampling can be seen as the C. elegans of quantum computing. (See, this paper.) Update (January 6, 2021): Tomorrow January, 7, 8:30 AM Israel time, I give a … Continue reading

Posted in Combinatorics, Computer Science and Optimization, Physics, Probability, Quantum | Tagged , | 12 Comments

Open problem session of HUJI-COMBSEM: Problem #4, Eitan Bachmat: Weighted Statistics for Permutations

This is a continuation of our series of posts on the HUJI seminar 2020 open problems. This time the post was kindly written by Eitan Bachmat who proposed the problem.  My summary: understanding of the distribution of largest increasing subsequences … Continue reading

Posted in Combinatorics, Guest blogger, Probability | Tagged | 4 Comments