Discovering of boundedness and continuity of random fields by means of partition entropic scheme

TL;DR

This paper introduces a novel partition entropic scheme to establish sufficient conditions for the boundedness and continuity of random fields, providing practical exponential tail estimates for their maxima.

Contribution

It develops new criteria based on a partition scheme similar to majorizing measures, with explicit exponential tail bounds for maxima of random fields.

Findings

New sufficient conditions for boundedness and continuity of random fields.

Explicit exponential tail estimates for the distribution of the maximum.

Applicable to statistical and Monte Carlo methods.

Abstract

We construct a new sufficient conditions for boundedness or continuity of arbitrary random fields relying on the so-called partition scheme, alike in the classical majorizing measure method. We deduce also the used in the practice (statistics, method Monte-Carlo etc.) exact exponential estimates for tail of distribution of maximum for random field satisfying formulated in this report conditions.