Category Archives: Probability

Benjamini and Mossel’s 2000 Account: Sensitivity of Voting Schemes to Mistakes and Manipulations

Here is a popular account by Itai Benjamini and Elchanan Mossel from 2000 written shortly after the 2000 US presidential election. Elchanan and Itai kindly agreed that I will publish it here,  for the first time, 20 years later!  I … Continue reading

Posted in Combinatorics, Games, Probability, Rationality | Tagged , | 6 Comments

Test Your Intuition (46): What is the Reason for Maine’s Huge Influence?

Very quick updates: Corona: Israel is struggling with the pandemic with some successes,  some failures, and much debate. Peace: We have peace agreements now with several Arab countries, most recently with Sudan. This is quite stunning. Internal politics: As divided … Continue reading

Posted in Games, Probability, Statistics, Test your intuition | Tagged , | 6 Comments

This question from Tim Gowers will certainly cheeer you up! and test your intuition as well!

I've rolled a die and not looked at it yet. The statement, "If the number I rolled equals 2+2 then it equals 5," is … — Timothy Gowers (@wtgowers) October 18, 2020 Here is a tweet from Tim Gowers  It … Continue reading

Posted in Logic and set theory, Philosophy, Probability | Tagged | 12 Comments

Cheerful Test Your Intuition (#45): Survey About Sisters and Brothers

You survey many many school children and ask each one: Do you have more brothers than sisters? or more sisters than brothers? or the same number? Then you separate the boys’s answers from the girls’s answers Which of the following … Continue reading

Posted in Combinatorics, Probability, Riddles, Statistics, Test your intuition | Tagged | 7 Comments

To Cheer you up in Difficult Times 8: Nathan Keller and Ohad Klein Proved Tomaszewski’s Conjecture on Randomly Signed Sums

Today we talk about the paper, Proof of Tomaszewski’s Conjecture on Randomly Signed Sums, by Nathan Keller and Ohad Klein. Consider a unit vector That is . Consider all () signed sums where each is either 1 or -1. Theorem … Continue reading

Posted in Analysis, Combinatorics, Probability | Tagged , , | 11 Comments

To cheer you up in difficult times 3: A guest post by Noam Lifshitz on the new hypercontractivity inequality of Peter Keevash, Noam Lifshitz, Eoin Long and Dor Minzer

This is a guest post kindly contributed by Noam Lifshitz. My short introduction: There is nothing like a new hypercontractivity inequality to cheer you up in difficult times and this post describes an amazing new hypercontractivity inequality.  The post describes … Continue reading

Posted in Analysis, Combinatorics, Computer Science and Optimization, Guest post, Poetry, Probability | Tagged , , , , | 4 Comments

Trees not Cubes! Memories of Boris Tsirelson

This post is devoted to a few memories of Boris Tsirelson who passed away at the end of January. I would like to mention that a few days ago graph theorist Robin Thomas passed away after long battle with ALS. … Continue reading

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

Remarkable New Stochastic Methods in ABF: Ronen Eldan and Renan Gross Found a New Proof for KKL and Settled a Conjecture by Talagrand

  The main conjecture from Talagrand’s paper on boundaries and influences was settled by Ronen Eldan and Renan Gross. Their paper introduces a new powerful method to the field of analysis of Boolean functions (ABF). This post is devoted to … Continue reading

Posted in Analysis, Combinatorics, Probability | Tagged , , | 5 Comments

Hoi Nguyen and Melanie Wood: Remarkable Formulas for the Probability that Projections of Lattices are Surjective

Following a lecture by Hoi Nguyen at Oberwolfach, I would like to tell you a little about the paper: Random integral matrices: universality of surjectivity and the cokernel by Hoi Nguyen and Melanie Wood. Two background questions: Hoi started with … Continue reading

Posted in Algebra, Combinatorics, Number theory, Probability | Tagged , | 6 Comments

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