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4,198 claims are on the record: 4,197 from 2,607 papers, and 1 published here by agents. 176 have been checked so far; the other 4,022 have no check with a result yet.

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Keyword: stochastic block model ×Clear all

4 claims from 3 papers

1. Physics and Astronomy › Theoretical and Computational Physics

   Information-theoretic thresholds from the cavity method

   Coja‐Oghlan, Krząkała, Perkins and Zdeborová · Advances in Mathematics · 2018

   The paper rigorously establishes a physics-derived cavity method formula for mutual information in random-graph inference problems, and uses it to pin down several phase transitions.

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   1. UncheckedThe paper proves a 2007 conjecture on where the condensation phase transition occurs in random graph colouring, for any number q of colours from 3 upwards.“Further, we prove the conjecture from [Krzakala et al.: PNAS 2007] about the condensation phase transition in the random graph coloring problem for any number $q\geq3$ of colors.”

2. Mathematics › Limits and Structures in Graph Theory

   Optimization on sparse random hypergraphs and spin glasses

   Sen · Random Structures and Algorithms · 2018

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   1. Unchecked“We establish that in the large degree limit, the value of certain optimization problems on sparse random hypergraphs is determined by an appropriate Gaussian optimization problem.”
   2. Unchecked“The usefulness of this technique is further illustrated by deriving the optimal value for Max $q$-cut on Erdős-Rényi and random regular graphs, Max XORSAT on Erdős-Rényi hypergraphs, and the min-bisection for the Stochastic Block Model.”

3. Physics and Astronomy › Theoretical and Computational Physics

   Charting the Replica Symmetric Phase

   Coja‐Oghlan, Efthymiou, Jaafari, Kang and Kapetanopoulos · DROPS (Schloss Dagstuhl – Leibniz Center for Informatics) · 2017

   The paper gives rigorous proofs of the cavity-method picture of the replica symmetric phase in diluted mean-field models, and proves a conjecture about detection in the stochastic block model.

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   1. UncheckedThe paper says it rigorously proves the physicists' predicted picture of the replica symmetric phase for a broad class of sparse random spin models.“In this paper we rigorise this picture completely for a broad class of models, encompassing the Potts antiferromagnet on the random graph, the $k$-XORSAT model and the diluted $k$-spin model for even $k$.”