# Adjacency Rules for Products of Stochastic Matrices

### Abstract

Infinite products of stochastic matrices arise in contexts such as statistical physics, computer engineering and distributed optimization. They describe the evolution of the distribution of states of a system or can be used to obtain a consensus between agents. The theory is relatively well-understood when the products are iterate of a single matrix, but is far more challenging when more matrices are involved. In this talk, I will describe a new approach to design families of stochastic matrices and the corresponding rules for their product. The approach relies on an associated graph, which we call Restricted Triangulated Laman graph, whose construction is inspired by classical rigidity theory. This approach guarantees convergence of the product and, unlike most other work in the field, allows us to obtain the limiting distribution explicitly. (Joint work with X. Chen)

### Biography

M.-A. Belabbas obtained his PhD degree in applied mathematics from Harvard University and his undergraduate degree from Ecole Centrale Paris, France, and Universite Catholique de Louvain, Belgium. He is currently an associate professor in the Electrical and Computer Engineering department at the University of Illinois, Urbana-Champaign and at the Coordinated Science Laboratory. His research interests are in Networked Control System, Stochastic control, Robotics and Geometric control theory.