Climbing down Gaussian peaks

• Robert J. Adler ^[1] ; Gennady Samorodnitsky ^[2]
  1. [1] Technion – Israel Institute of Technology

     Technion – Israel Institute of Technology

     Israel

     
  2. [2] Cornell University

     Cornell University

     City of Ithaca, Estados Unidos

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 45, Nº. 2, 2017, págs. 1160-1189
• Idioma: inglés
• DOI: 10.1214/15-AOP1083
• Enlaces
  • Texto completo
• Resumen

  • How likely is the high level of a continuous Gaussian random field on an Euclidean space to have a “hole” of a certain dimension and depth? Questions of this type are difficult, but in this paper we make progress on questions shedding new light in existence of holes. How likely is the field to be above a high level on one compact set (e.g., a sphere) and to be below a fraction of that level on some other compact set, for example, at the center of the corresponding ball? How likely is the field to be below that fraction of the level anywhere inside the ball? We work on the level of large deviations.