# Stochastic Geometry and Information Theory

Abstract:

This talk will give a survey of recent results on the interplay between stochastic geometry and information theory. First, we will show that stochastic geometry provides a natural way of defining and computing macroscopic properties of classical channels of network information theory. These macroscopic properties are obtained by some averaging over all node patterns found in a large random network of the Euclidean plane. We will discuss the implications of this spatial averaging viewpoint to wireless network design. Secondly, we will revisit some of the most basic capacity and error exponent questions of information theory in terms of random geometric objects living in Euclidean spaces with dimensions tending to infinity. This approach allows one to use the theory of large deviations to evaluate random coding error exponents in channels with additive stationary and ergodic noise.

Bio:

Francois Baccelli is a Professor and Research Director at the Ecole Normale Superieure in Paris, France. The Ecole Normale Superieure (ENS) is one of Europe's top research institutions, and the most prestigious "Grande Ecole" in France. The Computer Science department, known as the "Department d'Informatique" grew out of the Mathematics Department, and now has over 100 full-time researchers. ( http://www.di.ens.fr/WhatIsDI.html.en ) In addition to his position at ENS, Prof. Baccelli has held visiting positions including Fellow of the Isaac Newton Institute for Mathematical Sciences at Cambridge, and Miller Professor at UC Berkeley. He held a Eurandom Chair from the Eurandom Institute in the Netherlands, and since 2005 has been a member of the French Academy of Sciences. He has made fundamental mathematical contributions to Probability Theory, Stochastic Networks, and Information Theory, including foundational results in point processes, stochastic geometry and martingales. His results have had far reaching impact in communication theory, including multi-hop networks, wireless networks, and network simulation. He has been the recipient of the IEEE Communication Society's Best Tutorial Paper Award, the IBM Academic Award, the Grand Prix France Telecom prize from the French Academy of Sciences, and the Marcel Neuts Prize. He is the author of four text books widely used in classes in Engineering and Mathematics. He has over 100 publications in top international conferences and journals.