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Documents authored by Jaafari, Nor

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DOI: 10.4230/LIPIcs.APPROX-RANDOM.2017.40
Charting the Replica Symmetric Phase

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

Published in: LIPIcs, Volume 81, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)

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 non-rigorous 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').
Cite as

Amin Coja-Oghlan, Charilaos Efthymiou, Nor Jaafari, Mihyun Kang, and Tobias Kapetanopoulos. Charting the Replica Symmetric Phase. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 81, pp. 40:1-40:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{cojaoghlan_et_al:LIPIcs.APPROX-RANDOM.2017.40,
  author =	{Coja-Oghlan, Amin and Efthymiou, Charilaos and Jaafari, Nor and Kang, Mihyun and Kapetanopoulos, Tobias},
  title =	{{Charting the Replica Symmetric Phase}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)},
  pages =	{40:1--40:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-044-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{81},
  editor =	{Jansen, Klaus and Rolim, Jos\'{e} D. P. and Williamson, David P. and Vempala, Santosh S.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2017.40},
  URN =		{urn:nbn:de:0030-drops-75895},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2017.40},
  annote =	{Keywords: Random factor graph, bounds for condensation phase transition, Potts antiferromagnet, diluted k-spin model, stochastic block model}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2015.726
Local Convergence of Random Graph Colorings

Authors: Amin Coja-Oghlan, Charilaos Efthymiou, and Nor Jaafari

Published in: LIPIcs, Volume 40, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)

Abstract
Let G=G(n,m) be a random graph whose average degree d=2m/n is below the k-colorability threshold. If we sample a k-coloring Sigma of G uniformly at random, what can we say about the correlations between the colors assigned to vertices that are far apart? According to a prediction from statistical physics, for average degrees below the so-called condensation threshold d_c, the colors assigned to far away vertices are asymptotically independent [Krzakala et al: PNAS 2007]. We prove this conjecture for k exceeding a certain constant k_0. More generally, we determine the joint distribution of the k-colorings that Sigma induces locally on the bounded-depth neighborhoods of a fixed number of vertices.
Cite as

Amin Coja-Oghlan, Charilaos Efthymiou, and Nor Jaafari. Local Convergence of Random Graph Colorings. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 40, pp. 726-737, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{cojaoghlan_et_al:LIPIcs.APPROX-RANDOM.2015.726,
  author =	{Coja-Oghlan, Amin and Efthymiou, Charilaos and Jaafari, Nor},
  title =	{{Local Convergence of Random Graph Colorings}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)},
  pages =	{726--737},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-89-7},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{40},
  editor =	{Garg, Naveen and Jansen, Klaus and Rao, Anup and Rolim, Jos\'{e} D. P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2015.726},
  URN =		{urn:nbn:de:0030-drops-53321},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2015.726},
  annote =	{Keywords: Random graph, Galton-Watson tree, phase transitions, graph coloring, Gibbs distribution, convergence}
}
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