Technion Students Probability Seminar/ March 29 Two talks: Please see titles and abstracts below: ====================================== Date: 29 March 2011 Place: Bloomfield 526, Faculty of <IE@M> Time: 15:30-16:30 and 17:00-18:00 Speakers: Omer Bobrowski and Roman Berezin ======================= The Distance Function and the Topology of Random Geometric Complexes (Omer Bobrowski) In this talk we focus on the distance function from a random set of points $P$ in the Euclidean space. The distance function is continuous, however, it is not everywhere differentiable. Nevertheless, one can accurately define critical points and then apply Morse theory to it. We study the number of critical points in small neighborhoods around $P$. Specifically, we are interested in the case where the number of points in $P$ goes to infinity, and the size of the neighborhoods goes to zero. We present limit theorems for the number of critical points and show that it exhibits a phase transition, depending on how fast the size of the neighborhoods goes to zero. A similar phase transition was presented recently by Kahle & Meckes who studied the Betti-numbers of random geometric complexes. We show that this is more than just a coincidence, and discuss the connection between the distance function and geometric complexes. ======================== Survival and Extinction of the Contact Process with Rapid Stirring (Roman Berezin) Abstract: We study a nearest neighbour contact process fused with exclusion process in $d\geq 3$. It is known that the critical value of the birth rate of the contact process starting with a single particle, necessary for indefinite survival approaches $1$ as a suitable scaling parameter approaches infinity. The main point of interest is to find sharp asymptotic for how close this critical value is to $1$. -- Dmitry Ioffe Professor, Faculty of IE&M, Technion, Haifa 32000, Israel. phone: 972-4-8294413 fax: 972-4-8295688 e-mail: <ieioffe@ie.technion.ac.il> Probability at the Technion: <http://probability.technion.ac.il/> _______________________________________________ Probseminar mailing list <Probseminar@technion.ac.il> <http://iemm1.technion.ac.il/mailman/listinfo/probseminar> --------------------------------------------------------- Technion Math. Net (TECHMATH) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Rami Atar <atar@ee.technion.ac.il>