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

TL;DR

This paper investigates the reconstruction problem in a symmetric 2q-state model with multiple mutations, revealing that the Kesten-Stigum bound is not tight for q ≥ 4, through a nonlinear dynamical system analysis.

Contribution

It introduces a nonlinear second order dynamical system for the model and demonstrates the non-tightness of the Kesten-Stigum bound for q ≥ 4.

Findings

Kesten-Stigum bound is not tight for q ≥ 4

Constructed a nonlinear dynamical system for analysis

Revealed phase transition behavior in the model

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 $q \geq 4$.