Several Theorems About Probabilistic Limiting Expressions: The Gaussian free field, symmetric Pearcey process, and strong Szegő asymptotics

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Several Theorems About Probabilistic Limiting Expressions: The Gaussian free field, symmetric Pearcey process, and strong Szegő asymptotics

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Title: Several Theorems About Probabilistic Limiting Expressions: The Gaussian free field, symmetric Pearcey process, and strong Szegő asymptotics
Author: Kuan, Jeffrey
Citation: Kuan, 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.
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Abstract: 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.
Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA
Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:17467309
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