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

• Published in: Journal of statistical physics Vol. 170; no. 3; pp. 617 - 641
• Main Authors: Liu, Wenjian, Jammalamadaka, Sreenivasa Rao, Ning, Ning
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.02.2018; Springer; Springer Nature B.V
• Subjects: Analysis; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Community colleges; DYNAMICAL SYSTEMS; INFORMATION THEORY; Interdisciplinary subjects; MARKOV PROCESS; Markov processes; Mathematical and Computational Physics; Mutation; MUTATIONS; NONLINEAR PROBLEMS; Physical Chemistry; Physics; Physics and Astronomy; PROBABILITY; Quantum Physics; RANDOMNESS; Reconstruction; Social networks; Statistical analysis; Statistical Physics and Dynamical Systems; SYMMETRY; Theoretical; Tightness; Transition probabilities; 82B26; Markov random fields on trees; Distributional recursion; 82B20; Dynamical system; 60K35; Kesten–Stigum reconstruction bound
• ISSN: 0022-4715; 1572-9613
• DOI: 10.1007/s10955-017-1937-1

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 2 q -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 ≥ 4 .