Jinyoung Park

A reformulation of the discrete Convexity Conjecture via $k$-thresholds

We introduce the notion of"$k$-thresholds''and show that Talagrand's discrete convexity conjecture is equivalent to the assertion that, for some universal integer $k \ge 2$, the $k$-threshold of every increasing family is at most a universal constant times its expectation threshold. We prove a reduction theorem that bo...