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 $\mu$ be a distribution on the facets of $X$. Informally, we say $(X,\mu )$ is a path comp…