Date of Award
Doctor of Philosophy (PhD)
This dissertation establishes various small deviation inequalities for the largest eigenvalue of the β-Jacobi Ensemble when β ≥ 1. Upper bounds for the right and left tails are found be in line with the shape of the Tracy-Widom Distribution. From these small deviation bounds, an upper bound on the variance of the largest eigenvalue is derived. This bound is in accordance with known limit theorems.
Katz-Moses, Benjamin Fuller, "Small Deviations for the Beta Jacobi Ensemble" (2012). Mathematics Graduate Theses & Dissertations. 13.