Limit Theory for Random Cech Complexes

Wednesday, November 20, 2013 - 1:30pm - 2:30pm
Keller 3-180
Yogeshwaran Dhandapani (Technion-Israel Institute of Technology)
In this talk, I shall try to describe some asymptotic results for random Cech complexes. These shall concern thresholds for vanishing and formation of Homology groups as well as identify the limiting distribution of the Betti numbers under different regimes. I shall try to emphasize the usefulness of various stochastic geometric tools such as martingale techniques, stabilization theory, Palm formula et al in the context of random topology. Though most of the talk shall be restricted to the case of Poisson or i.i.d. point process, we shall briefly discuss extensions to general point processes too.