N ov 2 00 6 Shape of the ground state energy density of Hill ’ s equation with nice Gaussian potential
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چکیده
Consider Hill’s operator Q = − d2 dx2 + q(x) in which the potential q(x) is an almost surely continuous and rotation invariant Gaussian process on the circle x ∈ [0, 1). We prove a universality result for the shape of the probability density function of the ground state energy.
منابع مشابه
Shape of the ground state energy density of Hill ’ s equation with nice Gaussian potential
Consider Hill’s operator Q = − d2 dx2 + q(x) in which the potential q(x) is an almost surely continuous and rotation invariant Gaussian process on the circle x ∈ [0, 1). 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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تاریخ انتشار 2008