On the shape of the ground state eigenvalue density of a random Hill's equation

Santiago Cambronero, Brian Rider, José A. Ramı́rez

Type: Article

Publication Date: 2005-10-05

Citations: 17

DOI: https://doi.org/10.1002/cpa.20104

Abstract

Abstract Consider the Hill's operator Q = − d 2 / dx 2 + q ( x ) in which q ( x ), 0 ≤ x ≤ 1, is a white noise. Denote by f (μ) the probability density function of −λ 0 ( q ), the negative of the ground state eigenvalue, at μ. We prove the detailed asymptotics as μ → + ∞. This result is based on a precise Laplace analysis of a functional integral representation for f (μ) established by S. Cambronero and H. P. McKean in 5 . © 2005 Wiley Periodicals, Inc.

Locations

Communications on Pure and Applied Mathematics - View
arXiv (Cornell University) - PDF

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Works Cited by This (17)

Action	Title	Year	Authors
+	Handbook of Elliptic Integrals for Engineers and Physicists	1954	Paul F. Byrd Morris D. Friedman
+	Electron Levels in a One-Dimensional Random Lattice	1960	H. Frisch Seth Lloyd
+	Functiontheoretic properties of the discriminant of Hill's equation	1963	Harry Hochstadt
+ PDF Chat	Asymptotic analysis of Gaussian integrals, II: Manifold of minimum points	1981	Richard S. Ellis Jay Rosen
+ PDF Chat	Laplace approximations for sums of independent random vectors	1986	Erwin Bolthausen
+	The ground state eigenvalue of Hill's equation with white noise potential	1999	Santiago Cambronero H. P. McKean
+ PDF Chat	On spectra of the Schr�dinger operator with a white Gaussian noise potential	1977	Masatoshi Fukushima Shintaro Nakao
+ PDF Chat	Radon-Nikodym Derivatives of Gaussian Measures	1966	L. A. Shepp
+	A limit law for the ground state of Hill's equation	1994	H. P. McKean
+	The spectrum of Hill's equation	1975	H. P. McKean Pierre van Moerbeke