Browsing Mathematics Theses and Dissertations by Author "Sinclair, Christopher"

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  • Ensemble Averages of Assorted Log-Gas Models 
    Wolff, Elisha (University of Oregon, 2022-10-04)
    We use techniques in the shuffle and exterior algebras to present the partition functions for several log-gas models in terms of either the Hyperpfaffian or the Berezin integral of an appropriate alternating tensor. Our ...
  • On the Solvability of Beta-Ensembles when Beta is a Square Integer 
    Wells, Jonathan (University of Oregon, 2019-09-18)
    We use combinatorial identities in the shuffle and exterior algebra to present hyperpfaffian formulations of partition functions for ß-ensembles with arbitrary probability measure when ß is a square integer. This is an ...
  • Solvable Particle Models Related to the Beta-Ensemble 
    Shum, Christopher (University of Oregon, 2013-10-03)
    For beta > 0, the beta-ensemble corresponds to the joint probability density on the real line proportional to prod_{n > m}^N abs{x_n - x_m}^beta prod_{n = 1}^N w(x_n) where w is the weight of the system. It has the ...
  • The Combinatorics of log-Coulomb Gases in p-Fields 
    Webster, Joe (University of Oregon, 2021-09-13)
    This thesis is based on the article [16], which studies the integral? ? ?a? ?b? s ρ(x1,...,xN) max|xi −xj| min|xi −xj| |xi −xj| ij dx1 ...dxN KN i<j i<j i<j where K is an arbitrary p-field, ρ is a well-behaved function ...
  • The Distribution of the Cusped Hypocycloidal Mahler Measure 
    Hunter, Nathan (University of Oregon, 2022-10-26)
    We explore generalized Mahler measures associated to regions in the complex plane. These generalized Mahler measures describe the complexity of polynomials in C[x] by comparing the geometry of their roots to subsets of C. ...
  • Unimodal Levy Processes on Bounded Lipschitz Sets 
    Armstrong, Gavin (University of Oregon, 2018-09-06)
    We give asymptotics near the boundary for the distribution of the first exit time of the isotropic alpha-stable Levy process on bounded Lipschitz sets in real euclidean space. These asymptotics bear some relation to the ...

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