Abstract
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 scales as the string’s length , into a superdiffusion phase , 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.
- Received 16 April 2004
DOI:https://doi.org/10.1103/PhysRevE.70.015104
©2004 American Physical Society