Fully bilinear generic and lifted random processes comparisons

TL;DR

This paper introduces a fully bilinear comparison principle for random processes that enhances previous methods, integrates with lifting techniques, and generalizes classical comparison principles like Slepian's and Gordon's, supported by numerical validation.

Contribution

It presents a new fully bilinear comparison principle that improves upon prior comparison results and can be combined with lifting techniques, extending classical comparison principles.

Findings

The fully bilinear comparison is stronger than previous results.

The new principle can be integrated with lifting machinery.

Numerical experiments confirm the theoretical predictions.

Abstract

In our companion paper \cite{Stojnicgscomp16} we introduce a collection of fairly powerful statistical comparison results. They relate to a general comparison concept and its an upgrade that we call lifting procedure. Here we provide a different generic principle (which we call fully bilinear) that in certain cases turns out to be stronger than the corresponding one from \cite{Stojnicgscomp16}. Moreover, we also show how the principle that we introduce here can also be pushed through the lifting machinery of \cite{Stojnicgscomp16}. Finally, as was the case in \cite{Stojnicgscomp16}, here we also show how the well known Slepian's max and Gordon's minmax comparison principles can be obtained as special cases of the mechanisms that we present here. We also create their lifted upgrades which happen to be stronger than the corresponding ones in \cite{Stojnicgscomp16}. A fairly large collection of results obtained through numerical experiments is also provided. It is observed that these results are in an excellent agreement with what the theory predicts.