Quadratic Vector Equations on Complex Upper Half-Plane (Memoirs of the American Mathematical Society; Number 1261) by Oskari Heikki Ajanki, László Erdos, and Torben Krüger - 2019

American Mathematical Society, 2019. Paperback. New Book. Paperback. Ajanki, Erdos, and Krüger consider the nonlinear equation -1/m=z+Sm with a parameter z in a complex upper half plane, where S is a positivity preserving symmetric linear operator acting on bounded functions. They cover set-up and main results; local laws for large random matrices; existence, uniqueness, and L2-bound; properties of solutions; uniform bounds; regularity of solutions; perturbations when generating density is small; behavior of generating density where it is small; stability around small minima of generating density; and examples. (2019 Ringgold, Inc., Portland, OR)