Survival probabilities in time-dependent random walks.

@article{Nakar2004SurvivalPI,
  title={Survival probabilities in time-dependent random walks.},
  author={Ehud Nakar and Shahar Hod},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2004},
  volume={70 1 Pt 2},
  pages={
          016116
        }
}
  • E. Nakar, S. Hod
  • Published 8 March 2004
  • Mathematics
  • Physical review. E, Statistical, nonlinear, and soft matter physics
We analyze the dynamics of random walks in which the jumping probabilities are periodic time-dependent functions. In particular, we determine the survival probability of biased walkers who are drifted towards an absorbing boundary. The typical lifetime of the walkers is found to decrease with an increment in the oscillation amplitude of the jumping probabilities. We discuss the applicability of the results in the context of complex adaptive systems. 
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References

SHOWING 1-10 OF 40 REFERENCES
Time-dependent random walks and the theory of complex adaptive systems.
  • S. Hod
  • Mathematics
    Physical review letters
  • 2003
TLDR
The dynamics of random walks in which the jumping probabilities are time dependent are analyzed to reveal the underlying dynamics responsible for the phenomenon of self-segregation and clusters observed in the evolutionary minority game.
Statistics of Persistent Events in the Binomial Random Walk: Will the Drunken Sailor Hit the Sober Man?
The statistics of persistent events, recently introduced in the context of phase ordering dynamics, is investigated in the case of the one-dimensional lattice random walk in discrete time. We
Continuously variable survival exponent for random walks with movable partial reflectors.
TLDR
A one-dimensional lattice random walk with an absorbing boundary at the origin and a movable partial reflector is studied, suggesting a mechanism for nonuniversal kinetic critical behavior, observed in models with an infinite number of absorbing configurations.
Aspects and Applications of the Random Walk
Introductory comments the ubiquitous characteristic function asymptotic properties and the diffusion limit lattice walks boundaries and constraints multistate random walks selected applications.
Temporal oscillations and phase transitions in the evolutionary minority game.
  • E. Nakar, S. Hod
  • Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2003
TLDR
The temporal oscillations that characterize the system explain the transition in the global behavior from self-segregation to clustering in the R<1 case.
One-dimensional drift-diffusion between two absorbing boundaries: application to granular segregation
Motivated by a novel method for granular segregation, we analyse the one-dimensional drift-diffusion between two absorbing boundaries. The time evolution of the probability distribution and the rate
Random Walks, Critical Phenomena, and Triviality in Quantum Field Theory
The subject of this book is equilibrium statistical mechanics, in particular the theory of critical phenomena, and quantum field theory. The central theme is the use of random-walk representations as
Non-equilibrium critical phenomena and phase transitions into absorbing states
This review addresses recent developments in non-equilibrium statistical physics. Focusing on phase transitions from fluctuating phases into absorbing states, the universality class of directed
...
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