The Annals of Applied Probability

A positive temperature phase transition in random hypergraph 2-coloring

Victor Bapst, Amin Coja-Oghlan, and Felicia Raßmann

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Abstract

Diluted mean-field models are graphical models in which the geometry of interactions is determined by a sparse random graph or hypergraph. Based on a nonrigorous but analytic approach called the “cavity method”, physicists have predicted that in many diluted mean-field models a phase transition occurs as the inverse temperature grows from $0$ to $\infty$ [Proc. National Academy of Sciences 104 (2007) 10318–10323]. In this paper, we establish the existence and asymptotic location of this so-called condensation phase transition in the random hypergraph $2$-coloring problem.

Article information

Source
Ann. Appl. Probab., Volume 26, Number 3 (2016), 1362-1406.

Dates
Received: October 2014
Revised: March 2015
First available in Project Euclid: 14 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1465905006

Digital Object Identifier
doi:10.1214/15-AAP1119

Mathematical Reviews number (MathSciNet)
MR3513593

Zentralblatt MATH identifier
1343.05134

Subjects
Primary: 05C80: Random graphs [See also 60B20] 68Q87: Probability in computer science (algorithm analysis, random structures, phase transitions, etc.) [See also 68W20, 68W40] 05C15: Coloring of graphs and hypergraphs

Keywords
Discrete structures random hypergraphs phase transitions positive temperature

Citation

Bapst, Victor; Coja-Oghlan, Amin; Raßmann, Felicia. A positive temperature phase transition in random hypergraph 2-coloring. Ann. Appl. Probab. 26 (2016), no. 3, 1362--1406. doi:10.1214/15-AAP1119. https://projecteuclid.org/euclid.aoap/1465905006


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References

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