We continue our analysis of the number partitioning problem with n weights chosen i.i.d. from some fixed probability distribution with density \u00bd. In Part I of this work, we established the so-called local REM conjecture of Bauke, Franz and Mertens. Namely, we showed that, as n ! 1, the suitably rescaled energy spectrum above some fixed scale \u00ae tends to a Poisson process with density one, and the partitions corresponding to these energies\u00a0 become asymptotically uncorrelated. In this part, we analyze the number partitioning problem for energy scales \u00aen that grow with n, and show that the local REM conjecture holds as long as n\u00a11=4\u00aen ! 0, and fails if \u00aen grows like \u00b7n1=4 with \u00b7 > 0. We also consider the SK-spin glass model, and show that it has an analogous threshold: the local REM conjecture holds for energies of order o(n), and fails if the energies grow like \u00b7n with \u00b7 > 0.<\/p>\n","protected":false},"excerpt":{"rendered":"
We continue our analysis of the number partitioning problem with n weights chosen i.i.d. from some fixed probability distribution with density \u00bd. In Part I of this work, we established the so-called local REM conjecture of Bauke, Franz and Mertens. Namely, we showed that, as n ! 1, the suitably rescaled energy spectrum above some […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","footnotes":""},"msr-content-type":[3],"msr-research-highlight":[],"research-area":[13561],"msr-publication-type":[193716],"msr-product-type":[],"msr-focus-area":[],"msr-platform":[],"msr-download-source":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-317969","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-algorithms","msr-locale-en_us"],"msr_publishername":"","msr_edition":"Random Struct. 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