Definition and self-adjointness of the stochastic airy operator

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Abstract

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.

Original languageEnglish
Pages (from-to)695-711
Number of pages17
JournalMarkov Processes and Related Fields
Volume21
Issue number3P
Publication statusPublished - 2015

Keywords

  • Random Schrödinger operator
  • Self-adjointness
  • Sturm-Liouville operator

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistics and Probability

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