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Survival probabilities in time-dependent random walks
1The Racah Institute of Physics, The Hebrew University, Jerusalem 91904, Israel.
Summary
We studied random walks with time-dependent jumping probabilities. Increasing oscillation amplitude of these probabilities shortens walker lifetime near boundaries.
Area of Science:
- Statistical Mechanics
- Stochastic Processes
Background:
- Random walks are fundamental models in physics and computer science.
- Understanding walker dynamics is crucial for fields like finance and biology.
Purpose of the Study:
- To analyze random walk dynamics with time-dependent jumping probabilities.
- To determine the survival probability of biased walkers approaching an absorbing boundary.
Main Methods:
- Mathematical analysis of stochastic processes.
- Investigating periodic time-dependent functions for jumping probabilities.
- Calculating walker survival probability.
Main Results:
- Walker survival probability is influenced by periodic time-dependent jumping probabilities.
- Increased oscillation amplitude of jumping probabilities leads to decreased walker lifetime.
- The findings provide insights into the behavior of biased walkers.
Conclusions:
- The study quantifies the impact of oscillating jump rates on walker persistence.
- Results are relevant for modeling complex adaptive systems with dynamic environments.
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