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Category Archives: Probability
TYI38 Lior Kalai: Monty Hall Meets Survivor
Before moving to our riddle Breaking news: (added March 20, 2019) I am very happy to report that yesterday, March 19, 2019, Karen Uhlenbeck was awarded the 2019 Abel prize “for her pioneering achievements in geometric partial differential equations, gauge … Continue reading
Posted in Probability, Riddles, Test your intuition
Tagged Lior Kalai, Monty Hall problem, Survivor
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Test Your Intuition (or simply guess) 37: Arithmetic Progressions for Brownian Motion in Space
Consider a Brownian motion in three dimensional space. 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.) A 2-D picture; In … Continue reading
Konstantin Tikhomirov: The Probability that a Bernoulli Matrix is Singular
Konstantin Tikhomirov An old problem in combinatorial random matrix theory is cracked! Singularity of random Bernoulli matrices by Konstantin Tikhomirov Abstract: For each , let be an n×n random matrix with independent ±1 entries. We show that P( is singular}=, … Continue reading
Exciting Beginning-of-the-Year Activities and Seminars.
Let me mention two talks with very promising news by friends of the blog, Karim Adiprasito and Noam Lifshitz. As always, with the beginning of the academic year there are a lot of exciting activities, things are rather hectic around, … Continue reading
Posted in Combinatorics, Geometry, Probability
Tagged Dor Minzer, Eoin Long, Karim Adiprasito, Noam Lifshitz, Peter Keevash
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Duncan Dauvergne and Bálint Virág Settled the Random Sorting Networks Conjectures
A short summary: The beautiful decade-old conjectures on random sorting networks by Omer Angel, Alexander Holroyd, Dan Romik, and Bálint Virág, have now been settled by Duncan Dauvergne and Bálint Virág in two papers: Circular support in random sorting networks, by Dauvergne … Continue reading
Posted in Combinatorics, Probability, Updates
Tagged Bálint Virág, Dubcan Dauvergne, Random sorting networks
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Itai Benjamini: Coarse Uniformization and Percolation & A Paper by Itai and me in Honor of Lucio Russo
Here is another video of a smashing short talk by my dear friend Itai Benjamini with beautiful conjectures proposing an important new step in the connection between percolation and conformal geometry. Here is the link to Itai’s original paper Percolation … Continue reading
Bálint Virág: Random matrices for Russ
You can watch now all the videos for Russfest Elegance in Probability. Many great talks! I just watched Bálint Virág‘s lecture “Random matrices for Russ”. Highly recommended.
Posted in Combinatorics, Probability
Tagged Bálint Virág, random matrices, Russ Lyons
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TYI 31 – Rados Radoicic’s Rope Problem
Ropemaker (source) Rados Radoicic wrote me: “Several years back, I heard the following puzzle that turns out to be rather ‘classical’: “There are N ropes in a bag. In each step, two rope ends are picked uniformly at random, tied … Continue reading
Posted in Combinatorics, Probability, Test your intuition
Tagged Rados Radoicic, Test your intuition
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Elchanan Mossel’s Amazing Dice Paradox (your answers to TYI 30)
TYI 30 asked Elchanan Mossel’s Amazing Dice Paradox (that I heard from Yuval Peres yesterday) You throw a die until you get 6. What is the expected number of throws (including the throw giving 6) conditioned on the event that all throws … Continue reading
Posted in Combinatorics, Probability, Test your intuition
Tagged condition probability, Elchanan Mossel
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TYI 30: Expected number of Dice throws
Test your intuition: You throw a dice until you get 6. What is the expected number of throws (including the throw giving 6) conditioned on the event that all throws gave even numbers. follow-up post
