Person:

Kuan, Jeffrey

Certain probabilistic processes appear in the asymptotic scaling limit of many models. This thesis covers several theorems about such processes. Chapter 2 covers the Gaussian free field in interlacing particle systems, chapters 4 and 5 construct a non–commutative particle system and prove the Gaussian free field convergence. Chapter 3 shows the symmetric Pearcey process in a discrete–time interlacing particle system with a wall, and chapter 6 shows Strong Szegő asymptotics for the Riemann ζ funcion.