On Tail Triviality of Negatively Dependent Stochastic Processes

• Main Authors: Alishahi, Kasra, Barzegar, Milad, Zamani, Mohammadsadegh
• Format: Journal Article
• Language: English
• Published: 08-03-2022
• Subjects: Mathematics - Probability
• DOI: 10.48550/arxiv.2203.03935

We prove that every negatively associated sequence of Bernoulli random
variables with "summable covariances" has a trivial tail sigma-field. A
corollary of this result is the tail triviality of strongly Rayleigh processes.
This is a generalization of a result due to Lyons which establishes tail
triviality for discrete determinantal processes. We also study the tail
behavior of negatively associated Gaussian and Gaussian threshold processes. We
show that these processes are tail trivial though they do not in general
satisfy the summable covariances property. Furthermore, we construct negatively
associated Gaussian threshold vectors that are not strongly Rayleigh. This
identifies a natural family of negatively associated measures that is not a
subset of the class of strongly Rayleigh measures.