Author

Ruben Ascoli

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Preprint Oct 2026

Satisfiability and freezing in random integer programs

We study a model of a random centrally symmetric polytope and ask about the existence of points in the polytope with non-zero, integer coordinates. Our main results are the location of a sharp threshold for the existence of these integer points, a characterization of the typical empirical distribution of their coordina...

Dylan J. Altschuler, Ruben Ascoli, Will Perkins · 0 citations

Preprint Aug 2026

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...

Ruben Ascoli, Xiaoyu He, Jinyoung Park et al. · 5 citations · ⚡2