Probability Seminar

Swee Hong ChanUniversity of California, Los Angeles
Sorting probability for Young diagrams

Monday, September 13, 2021 - 3:45pm
Malott 406

Abstract: Can you always find two elements x,y of a partially ordered set, such that, the probability that x is ordered before y when the poset is ordered randomly, is between 1/3 and 2/3? This is the celebrated 1/3-2/3 Conjecture, which has been called "one of the most intriguing problems in the combinatorial theory of posets". We will explore this conjecture for posets that arise from (skew-shaped) Young diagrams, where total orderings of these posets correspond to standard Young tableaux. We will show that that these probabilities are arbitrarily close to 1/2, by using random walk estimates and the state-of-the-art hook-length formulas of Naruse. This is a joint work with Igor Pak and Greta Panova. This talk is aimed at a general audience.