Details

Autor(en) / Beteiligte

• Cambronero, Santiago
• Rider, Brian
• Ramírez, José

Titel

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

Ist Teil von

• Communications on pure and applied mathematics, 2006-07, Vol.59 (7), p.935-976

Ort / Verlag

Hoboken: Wiley Subscription Services, Inc., A Wiley Company

Erscheinungsjahr

2006

Link zum Volltext

Quelle

Wiley Online Library Journals Frontfile Complete

Beschreibungen/Notizen

• Consider the Hill's operator Q = −d2/dx2 + q(x) in which q(x), 0 ≤ x ≤ 1, is a white noise. Denote by f(μ) the probability density function of −λ0(q), the negative of the ground state eigenvalue, at μ. We prove the detailed asymptotics $$ f(\mu) = {4 \over 3\pi} \mu \, {\rm exp} \left[-{8 \over 3}\mu^{8/3} - {1 \over 2}\mu^{1/2} \right] (1 + o(1)) $$ 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.