Shayan Oveis Gharan

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20242026

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math.CO2025

Trickle-down Theorems via C-Lorentzian Polynomials II: Pairwise Spectral Influence and Improved Dobrushin's Condition

Jonathan Leake, Shayan Oveis Gharan

Let $μ$ be a probability distribution on a multi-state spin system on a set $V$ of sites; equivalently, a $d$ -partite simplicial complex with distribution $μ$ on maximal faces. For…

math.CO2025

Optimal Trickle-Down Theorems for Path Complexes via C-Lorentzian Polynomials with Applications to Sampling and Log-Concave Sequences

Jonathan Leake, Kasper Lindberg, Shayan Oveis Gharan

Let $X$ be a $d$ -partite $d$ -dimensional simplicial complex with parts $T_{1}, \dots, T_{d}$ and let $μ$ be a distribution on the facets of $X$ . Informally, we say $(X, μ)$ is a path comp…

math.CO2025

Unweighted One-Sided Code Sparsifiers and Thin Subgraphs

Shayan Oveis Gharan, Arvin Sahami

For a linear code $C \subseteq F_{2}^{n}$ and $α \in [0, 1]$ , call a set $S \subseteq [n]$ an (unweighted) one-sided $α$ -sparsifier of $C$ if for all $c \in…