Asymptotic Measures and Links in Simplicial Complexes

Abstract

We introduce canonical measures on a locally finite simplicial complex K and study their asymptotic behavior under infinitely many barycentric subdivisions. We prove that the simplices of each dimension in $$\text {Sd}^d(K)$$ equidistribute in |K| with respect to the Lebesgue measure as d grows to $$+\infty $$ and then prove that their asymptotic link and dual block are universal.