2 citations · 2 across the 3 of their papers we have counts for
4 papers
On a set of transformations of Gaussian random functions
A. I. Nazarov
We consider a set of one-dimensional transformations of Gaussian random functions. Under natural assumptions we obtain a connection between -small ball asymptotics of the tran…
Log-Level Comparison Principle for Small Ball Probabilities
A. I. Nazarov
We prove a new variant of comparison principle for logarithmic -small ball probabilities of Gaussian processes. As an application, we obtain logarithmic small ball asymptotics…
Exact L_2-small ball asymptotics of Gaussian processes and the spectrum of boundary value problems with "non-separated" boundary conditions
A. I. Nazarov
We sharpen a classical result on the spectral asymptotics of the boundary value problems for self-adjoint ordinary differential operator. Using this result we obtain the exact $L_2…
On S.L. Tabachnikov's conjecture
A. I. Nazarov, F. V. Petrov
S. L. Tabachnikov's conjecture is proved: for any closed curve lying inside convex closed curve the mean absolute curvature exceeds if . An ine…