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Phase transition in random walks with long-range correlations
1The Racah Institute of Physics, The Hebrew University, Jerusalem 91904, Israel.
Summary
Random walks with long-term memory exhibit a phase transition from normal diffusion to superdiffusion. This transition occurs when the correlation strength surpasses a critical threshold, impacting various data types.
Area of Science:
- Statistical Physics
- Complex Systems
- Information Theory
Background:
- Correlated sequences and their dynamics are crucial in understanding complex systems.
- Random walks are fundamental models for diffusion processes.
- Long-term memory effects can significantly alter system dynamics.
Purpose of the Study:
- To analyze the dynamics of random walks with long-term memory (binary chains with long-range correlations).
- To investigate the conditions under which a dynamical phase transition occurs.
- To explore the applicability of the model to diverse real-world data.
Main Methods:
- Modeling binary chains where bit probability depends on preceding unities.
- Analyzing the scaling of variance D(L) with string length L.
- Demonstrating result generality across alternative models.
Main Results:
- A dynamical phase transition from normal diffusion to superdiffusion was identified.
- Superdiffusion occurs when correlation strength exceeds a critical value (D(L) ~ L^alpha, alpha>1).
- The model's generality was confirmed.
Conclusions:
- The study reveals a critical transition in correlated random walks.
- Findings have implications for analyzing DNA sequences, texts, and financial data.
- The model provides a framework for understanding systems with long-range correlations.
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