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/>
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