Generic proving of replica symmetry breaking
Abstract
We study the replica symmetry breaking (rsb) concepts on a generic level through the prism of recently introduced interpolating/comparison mechanisms for bilinearly indexed (bli) random processes. In particular, Stojnicnflgscompyx23 introduced a fully lifted (fl) interpolating mechanism and Stojnicsflgscompyx23 developed its a stationarized fully lifted (sfl) variant. Here, we present a sfl matching mechanism that shows that the results obtained in Stojnicnflgscompyx23,Stojnicsflgscompyx23 completely correspond to the ones obtained by a statistical physics replica tool with the replica symmetry breaking (rsb) form suggested by Parisi in Par79,Parisi80,Par80. The results are very generic as they allow to handle pretty much all bilinear models at once. Moreover, given that the results of Stojnicnflgscompyx23,Stojnicsflgscompyx23 are extendable to many other forms, the concepts presented here automatically extend to any such forms as well.
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