In this work we explore a connection between some high dimensional asymptotic problems and random matrix theory. In the first part, we establish a link between the Wishart ensemble and random critical points of holomorphic sections over complex projective space and use this to establish asymptotics on the average number of them. In the second part of this work, we further explore the link between the Gaussian Elliptic Ensemble and the average number of equilibrium points for a class of random Gaussian ordinary differential equations as established in Fyodorov. We use this link to establish asymptotics on the average number of stable equilibrium points for this class of random Gaussian ordinary differential equations.

Last modified

• 11/19/2019

Creator

• Xavier Eduardo Garcia

DOI

• https://doi.org/10.21985/n2-0bwp-7183

Subject

• Mathematics

Keyword

• High Dimensional
• Complex Geometry
• Differential Equations
• Probability Theory

Date created

• 2018-01-01

Resource type

• Dissertation

Rights statement

• In Copyright