Sensing, Signals, and Communications Seminar - Francois Baccelli

Apr 29

Friday, April 29, 2016

10:00 am - 11:15 am
Gross Hall 330


Francois Baccelli

This talk will survey recent results on Boolean stochastic geometry in high dimensional Euclidean spaces.A Boolean model in $\R^n$ consists of a homogeneous Poisson point process in $\R^n$ and of independent and identically distributed random closed sets of $\R^n$ centered on each atom of this point process.The Shannon regime features a family of Boolean models indexed by $n \ge 1$, where the $n$-th model has a Poisson point process of intensity $e^{n \rho}$ and random compact sets with diameter of order $\sqrt{n}$, and lets $n$ tend to $\infty$. A typical example is that where each random compact set is an $n$ ball of radius distributed like $\bar X_n \sqrt{n}$, with $\bar X_n$ satisfying a large deviations principle.The main focus of the talk will be on the asymptotic behavior of classical Boolean stochastic geometry quantities, like volume fraction, percolation threshold or mean cluster size, in this Shannon regime.The analysis of this asymptotic regime is motivated by problems in information theory, and leads to new results on error exponents, which describe the rate of decay to 0 of the probability of decoding error in channel coding. This regime is also of interest in machine learning.Joint work with V. Anantharam. François Baccelli is Simons Math+X Chair in Mathematics and ECE at UT Austin.


Dawn, Ariel