Upper tail probability estimates of suprema of Gaussian processes by matrices-A number theoretic example

Source abstract

We prove new lower bounds for the upper tail probabilities of suprema of Gaussian processes. We introduce a proper matrix approach. This is continuing recent works of the author on deviations of suprema and decoupling inequalities for parametrized families of Gaussian processes. An application is given to a number theoretic example related to Wintner random Möbius function.