### 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 language | English |
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Pages (from-to) | 695-711 |

Number of pages | 17 |

Journal | Markov Processes and Related Fields |

Volume | 21 |

Issue number | 3P |

Publication status | Published - 2015 |

### Keywords

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

### ASJC Scopus subject areas

- Applied Mathematics
- Statistics and Probability

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## Cite this

Minami, N. (2015). Definition and self-adjointness of the stochastic airy operator.

*Markov Processes and Related Fields*,*21*(3P), 695-711.