Category Archives: Probability

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

Posted on August 1, 2020 by

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

Posted on May 8, 2020 by

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

Posted on April 3, 2020 by

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

Posted on February 28, 2020 by

  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

Posted on February 17, 2020 by

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.

Posted on January 24, 2020 by

  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?

Posted on December 2, 2019 by

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

Posted on October 30, 2019 by

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

Posted on October 13, 2019 by

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

Posted on September 17, 2019 by

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