2003/11/20 by Shahar Hod, Uri Keshet · 5 citations
Biochemistry, Genetics and Molecular Biology · Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #Fractal and DNA sequence analysis #Theoretical and Computational Physics #cond-mat.stat-mech #nlin.SI #physics.bio-ph #physics.data-an #q-bio.GN
paper · pdf · doi:10.1103/physreve.70.015104
published as Phys. Rev. E 70, Rapid Communication, 015104 (2004). · 4 pages, 4 figures
arxiv created 2003/11/20 · openalex publication_date 2004/07/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Motivated by recent results in the theory of correlated sequences, we analyze the dynamics of random walks with long-term memory (binary chains with long-range correlations). In our model, the probability for a unit bit in a binary string depends on the fraction of unities preceding it. We show that the system undergoes a dynamical phase transition from normal diffusion, in which the variance D(L) scales as the string's length L, into a superdiffusion phase ( D(L) approximately Lalpha,alpha>1), when the correlation strength exceeds a critical value. We demonstrate the generality of our results with respect to alternative models, and discuss their applicability to various data, such as coarse-grained DNA sequences, written texts, and financial data.