Survival probabilities of history-dependent random walks

2005/06/02 by Uri Keshet, Shahar Hod
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.72.046144

published as Phys. Rev. E 72, 046144 (2005) · 3 pages, 2 figures

arxiv created 2005/06/02 · openalex publication_date 2005/10/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We analyze the dynamics of random walks with long-term memory (binary chains with long-range correlations) in the presence of an absorbing boundary. An analytically solvable model is presented, in which a dynamical phase transition occurs when the correlation strength parameter \ensuremathμ reaches a critical value \ensuremathμ_c. For strong positive correlations, \ensuremathμ>\ensuremathμ_c, the survival probability is asymptotically finite, whereas for \ensuremathμ<\ensuremathμ_c it decays as a power law in time (chain length).

Citations

• Phase transition in random walks with long-range correlations
• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Stochastic Processes in Physics and Chemistry