Master’s Thesis
Spectral Independence
Supervised by Kasra Alishahi at Sharif University of Technology.
Abstract: In this thesis we discuss the notion of spectral independence and its generalization, entropic independence. As examples of the application of these notions we will discuss rapid mixing of the matroid basis exchange walk and Markov chains for sampling from DPPs and the monomer-dimer system. Finally, we will use the stochastic localization framework to provide easier proofs for theorems related to spectral and entropic independence.