Shape of the ground state energy density of Hill's equation with nice Gaussian potential

Details Shape of the ground state energy density of Hill's equation with nice Gaussian potential Shape of the ground state energy density of Hill's equation with nice Gaussian potential

2006-11-18

arxiv.org/abs/math/0611555v2

Mathematics

Probability

19 pages, revised intro

Scientific paper

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.

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