Phd Thesis Defense : Records of stationary processes and unimodular graphs

Speaker : Bharath Roy Choudhury
Date: 18/09/2023
Time: 2:00 pm - 5:00 pm
Location: Inria, salle Gilles Hahn


Consider a navigation rule defined on a graph that maps every vertex of
the graph to a vertex in such a way that the navigation rule commutes
with every automorphism of the graph. It is to say that the navigation
rule applied to the vertices remains the same after taking any
automorphism of the graph. Such a navigation rule is said to have the
covariance property. This study delves into a collection of such
covariant navigation rules, indexed by locally finite graphs, and
subject to a measurability condition. This ensemble of rules is termed a
vertex-shift. More generally, one can consider vertex-shifts on
networks, graphs that have labels on edges and on vertices. A
vertex-shift induces a dynamic on the space of locally finite rooted
networks. The central focus of this work lies in investigating the
dynamic associated to a specific navigation rule called the record
vertex-shift. It is defined on the trajectories of any one dimensional
discrete random walk whose increments have finite mean and the random
walk can jump only one step to the left. Additionally, the work includes
several notable results concerning record vertex-shifts applied to
processes with stationary increments. The thesis also contains results
on more general vertex-shifts on unimodular networks.