A large deviation view of \emph{stationarized} fully lifted blirp interpolation

TL;DR

This paper extends large deviation principles to stationarized bilinearly indexed random processes with fully lifted interpolation, enabling analysis of atypical structures like local entropies and solution clustering in complex random optimization problems.

Contribution

It introduces a large deviation framework for stationarized fully lifted blirp interpolation, broadening applicability to atypical random structures and providing elegant fundamental relations.

Findings

Extended large deviation principles to stationarized blirp processes.

Analyzed local entropies and solution clustering in complex random problems.

Derived elegant fundamental relations for interpolating parameters.

Abstract

We consider \emph{bilinearly indexed random processes} (blirp) and study their interpolating comparative mechanisms. Generic introduction of the \emph{fully lifted} (fl) blirp interpolation in [105] was followed by a corresponding stationarization counterpart in [103]. A \emph{large deviation} upgrade of [105] introduced in companion paper [106] is complemented here with the corresponding one of [103]. Similarly to [106], the mechanism that we introduce extends the range of [103]'s applicability so that it encompasses random structures \emph{atypical} features. Among others these include the \emph{local entropies} (LE) which explain atypical solutions clusterings in hard random optimization problems believed to be directly responsible for the presumable existence of the so-called \emph{computational gaps}. Moreover (and similar to [105]), despite on occasion somewhat involved technical considerations, the final forms of the uncovered fundamental interpolating parameters relations are rather elegant and as such provide a valuable tool readily available for further use.