# Survival probabilities of history-dependent random walks Academic Article

•
• Overview
•
• Research
•
•
• View All
•

### 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 $\ensuremath{\mu}$ reaches a critical value ${\ensuremath{\mu}}_{c}$. For strong positive correlations, $\ensuremath{\mu}>{\ensuremath{\mu}}_{c}$, the survival probability is asymptotically finite, whereas for $\ensuremath{\mu}<{\ensuremath{\mu}}_{c}$ it decays as a power law in time (chain length).

### publication date

• January 1, 2005