Charting the replica symmetric phase

Amin Coja-Oghlan, Charilaos Efthymiou, Nor Jaafari, Mihyun Kang, Tobias Kapetanopoulos

Research output: Chapter in Book/Report/Conference proceedingConference paperpeer-review

Abstract

Random graph models and associated inference problems such as the stochastic block model play an eminent role in computer science, discrete mathematics and statistics. Based on nonrigorous arguments physicists predicted the existence of a generic phase transition that separates a "replica symmetric phase" where statistical inference is impossible from a phase where the detection of the "ground truth" is information-theoretically possible. In this paper we prove a contiguity result that shows that detectability is indeed impossible within the replica-symmetric phase for a broad class of models. In particular, this implies the detectability conjecture for the disassortative stochastic block model from [Decelle et al.: Phys. Rev. E 2011]. Additionally, we investigate key features of the replica symmetric phase such as the nature of point-to-set correlations ('reconstruction').
Original languageEnglish
Title of host publicationLeibniz International Proceedings in Informatics, LIPIcs
Pages1-17
VolumeVolume 81
ISBN (Electronic)978-395977044-6
DOIs
Publication statusPublished - 2017
Event21st International Workshop on Randomization and Computation: RANDOM 2017 - Berkeley, United States
Duration: 16 Aug 201718 Aug 2017

Conference

Conference21st International Workshop on Randomization and Computation
Country/TerritoryUnited States
CityBerkeley
Period16/08/1718/08/17

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