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Phase transition in random walks with long-range correlations.

Shahar Hod1, Uri Keshet

  • 1The Racah Institute of Physics, The Hebrew University, Jerusalem 91904, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 25, 2004
PubMed
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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.

Related Experiment Videos

  • 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.