Mathematics – Probability
Scientific paper
2006-11-18
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.
Ramirez Jose A.
Rider Brian
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