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.
|ジャーナル||Markov Processes and Related Fields|
|出版物ステータス||Published - 2015|
ASJC Scopus subject areas
- Applied Mathematics
- Statistics and Probability