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Author ORCID Identifier
0009-0003-9159-2602
Date Available
9-1-2026
Year of Publication
2026
Document Type
Doctoral Dissertation
Degree Name
Doctor of Philosophy (PhD)
College
Arts and Sciences
Department/School/Program
Mathematics
Faculty
Peter Hislop
Faculty
Bert Guillou
Abstract
We study a collection of discrete Schrodinger Operators with random potentials through the lens of global and local eigenvalue spacings. We discuss the three models: the standard scaled disorder Anderson Model, the Anderson-Bernoulli Polymer Model, and the Discrete Fractional Laplacian Anderson Model. First, we discuss the scaled disorder case using the invariant measure and its application to the density of states in the weak disorder limit. We also prove the limit of the local and global eigenvalue spacings in the non random case, and demonstrate numerically how randomness affects the eigenvalue spacings. We then discuss a special family of random polymer models and construct the critical energies, which are special values where the system goes from localization to delocalization. We also numerically verify our results against the literature. We then go into detail about the discrete fractional Laplacian. Here, we prove numerical estimates consistent with the literature, and use the Toeplitz structure of the approximating matrices to compute the local and global eigenvalue spacing distributions.
Digital Object Identifier (DOI)
https://doi.org/10.13023/etd.2026.342
Archival?
Archival
Recommended Citation
Hammer, Kyle E., "Eigenvalue Spacing Distributions and the Weak Disorder Limit for Random Schrodinger Operators" (2026). Theses and Dissertations--Mathematics. 132.
https://uknowledge.uky.edu/math_etds/132
