Algebraic Graph Theory Seminar - Hajime Tanaka

Title: Scaling limits for the Gibbs states on distance-regular graphs with classical parameters

Abstract:

Limits of the normalized spectral distributions and other related probability distributions of families of graphs have been studied in the context of quantum probability theory as analogues of the central limit theorem. First I will review some of the previous work by Hora, Obata, and others, focusing on the case of distance-regular graphs, and emphasizing how the theory is related to the Terwilliger algebra. I will then discuss distance-regular graphs with classical parameters where the base q is unequal to 1. Examples include the Grassmann graphs, dual polar graphs, and so on. I will give a classification of the possible limits in terms of the classical parameters.