The Tightness of the Kesten-Stigum Reconstruction Bound of Symmetric Model with Multiple Mutations

Abstract

It is well known that reconstruction problems, as the interdisciplinary subject, have been studied in numerous contexts including statistical physics, information theory and computational biology, to name a few. We consider a $2q$-state symmetric model, with two categories of $q$ states in each category, and 3 transition probabilities: the probability to remain in the same state, the probability to change states but remain in the same category, and the probability to change categories. We construct a nonlinear second order dynamical system based on this model and show that the Kesten-Stigum reconstruction bound is not tight when $q\ge 4$.

arXiv commentAccepted, to appear Journal of Statistical Physics

References in corpus (13)

• Algorithmic barriers from phase transitions
• Reconstruction on trees and spin glass transition
• Fate of Zero-Temperature Ising Ferromagnets
• On the freezing of variables in random constraint satisfaction problems
• Perfect simulation for interacting point processes, loss networks and Ising models
• Coarsening in the q-State Potts Model and the Ising Model with Globally Conserved Magnetization
• Reconstruction of Random Colourings
• Geometry of contours and Peierls estimates in d=1 Ising models
• The restriction of the Ising model to a layer
• Periodic striped ground states in Ising models with competing interactions
• Zero-Temperature Coarsening in the 2d Potts Model
• Universal finite size corrections and the central charge in non solvable Ising models
• Phase transition for the mixing time of the Glauber dynamics for coloring regular trees

Cited by in corpus (3)

• Typology of phase transitions in Bayesian inference problems
• Large Degree Asymptotics and the Reconstruction Threshold of the Asymmetric Binary Channels
• Big Data Information Reconstruction on an Infinite Tree for a $4\times 4$-state Asymmetric Model with Community Effects