The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 26, Number 3 (2016), 1362-1406.
A positive temperature phase transition in random hypergraph 2-coloring
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.
Ann. Appl. Probab., Volume 26, Number 3 (2016), 1362-1406.
Received: October 2014
Revised: March 2015
First available in Project Euclid: 14 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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