Research on Bruhat-Tits method in Machine Learning 2024 part6

Geometric branching operators on the Bruhat-Tits building associated to the symplectic group

Authors: Tal Nelken

Abstract: In this thesis we study geometric branching operators on simplices in the (affine) Bruhat-Tits building associated to the symplectic group over a local field. We use these operators to study the simple random walk on the building’s vertices. This work lays the foundations for studying the total-variation cutoff phenomenon for simple random walk on Ramanujan complexes of type C~n (n≥2).