Definition and self-adjointness of the stochastic airy operator

研究成果: Article査読

5 被引用数 (Scopus)

抄録

In this note, it is shown that the stochastic Airy operator, which is the "Schrödinger operator" on the half-line whose potential term consists of Gaussian white noise plus a linear term tending to †∞, can naturally be defined as a generalized Sturm-Liouville operator and that it is self-adjoint and has purely discrete spectrum with probability one. Thus "stochastic Airy spectrum" of Ramírez, Rider and Virág is the spectrum of an operator in the ordinary sense of the word.

本文言語English
ページ(範囲)695-711
ページ数17
ジャーナルMarkov Processes and Related Fields
21
3P
出版ステータスPublished - 2015

ASJC Scopus subject areas

  • 統計学および確率
  • 応用数学

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