Shape of the ground state energy density of Hill's equation with nice Gaussian potential
Abstract
Description
Consider Hill's operator Q = -D^2 + q(x) in which the potential q(x) is an almost surely continuous and rotation invariant Gaussian process on the circle of perimeter one. Viewing the classical Riccati map as a change of measure, we establish functional integral formulas for the probability density function of the ground state energy and also determine the density's shape.
19 pages, revised intro
19 pages, revised intro