Tokyo Probability Seminar

Seminar information archive ~04/13Next seminarFuture seminars 04/14~

Date, time & place Monday 16:00 - 17:30 126Room #126 (Graduate School of Math. Sci. Bldg.)
Organizer(s) Makiko Sasada, Shuta Nakajima

2018/10/22

16:00-17:30   Room #126 (Graduate School of Math. Sci. Bldg.)
Trinh Khanh Duy (Tohoku University)
Limit theorems for random geometric complexes in the critical regime (ENGLISH)
[ Abstract ]
Geometric complexes (eg. Cech complexes or Rips complexes) are simplicial complexes defined on a finite set of points in a Euclidean space together with a radius parameter, which can be viewed as a higher dimensional generalization of geometric graphs. This talk concerns with random geometric complexes built over binomial point processes (collections of iid points). Like random geometric graphs, there are three regimes (subcritical(or dust, sparse) regime, critical (or thermodynamic) regime and supercritical regime) which are divided according the growth of the radius parameters in which the limiting behavior of random geometric complexes is totally different. This talk introduces some results on the strong law of large numbers and a central limit theorem in the critical regime.