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Our companion paper \cite{Stojnicnflgscompyx23} introduced a very powerful\emph{fully lifted} (fl) statistical interpolating/comparison mechanism forbilinearly indexed random processes. Here, we present a particular realizationof such fl mechanism that relies on a stationarization along the interpolatingpath concept. A collection of very fundamental relations among theinterpolating parameters is uncovered, contextualized, and presented. As a nicebonus, in particular special cases, we show that the introduced machineryallows various simplifications to forms readily usable in practice. Given howmany well known random structures and optimization problems critically rely onthe results of the type considered here, the range of applications is prettymuch unlimited. We briefly point to some of these opportunities as well.

Bilinearly indexed random processes -- \emph{stationarization} of fully lifted interpolation