Borodin, AlexeiYau, Horng-TzerBloemendal, AlexanderKuan, Jeffrey2015-07-172015-052015-04-302015Kuan, Jeffrey. 2015. Several Theorems About Probabilistic Limiting Expressions: The Gaussian free field, symmetric Pearcey process, and strong Szegő asymptotics. Doctoral dissertation, Harvard University, Graduate School of Arts & Sciences.http://nrs.harvard.edu/urn-3:HUL.InstRepos:17467309Certain 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.application/pdfenMathematicsThesis or Dissertation2015-07-17