Asymptotic topology of random subcomplexes in a finite simplicial complex

Abstract

We consider a finite simplicial complex $K$ together with its successive barycentric subdivisions $S{d}^d(K),d\ge 0,$ and study the expected topology of a random subcomplex in $S{d}^d(K),d\gg 0$. We get asymptotic upper and lower bounds for the expected Betti numbers of those subcomplexes, together with the average Morse inequalities and expected Euler characteristic.

References in corpus (2)

• Suspensions of homology spheres
• Universal components of random nodal sets