RUS  ENG
Full version
JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2023 Volume 525, Pages 122–133 (Mi znsl7372)

On the mm-entropy of distributions of Gaussian processes

A. A. Tadevosian

Saint Petersburg State University

Abstract: For a wide class of Banach spaces with Gaussian measure, it is shown that their Shannon entropy (mm-entropy) is closely related to the entropy of the corresponding kernel's ball and behaves in a certain range in the same way as the logarithm of the measure of small balls. The obtained results generalize the recent results of A. M. Vershik and M. A. Lifshits.

Key words and phrases: Gaussian measures, mm-entropy, entropy of compacts.

Received: 30.09.2023



© Steklov Math. Inst. of RAS, 2024