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Category Archives: Probability
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
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 Michel Talagrand, Renan Gross, Ronen Eldan
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 Hoi Nguyen, Melanie Wood
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 Test your intuition
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 discrete cube, random walk, Test your intuition
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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 Bhargav Narayanan, Jeff Kahn, Jinyoung Park, Keith Frankston
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 Google, Henri Poincaré, quantum supremacy
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
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
