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Updated: Sep 4, 2025
04:13
Using a Real-Time Locating System to Measure Walking Activity Associated with Wandering Behaviors Among Institutionalized Older Adults
Published on: February 8, 2019
6.8K
Complete visitation statistics of one-dimensional random walks.
Léo Régnier1, Maxim Dolgushev1, S Redner2
1Laboratoire de Physique Théorique de la Matière Condensée, CNRS/Sorbonne University, 4 Place Jussieu, 75005 Paris, France.
Physical Review. E
|July 20, 2022
Summary
We developed a framework to analyze random walk statistics, revealing temporal correlations in site visitation. This non-Markovian behavior impacts understanding of trapping problems and other stochastic processes.
Area of Science:
- Statistical Mechanics
- Probability Theory
- Stochastic Processes
Background:
- Random walks are fundamental models in statistical physics.
- Understanding site visitation statistics is crucial for various applications.
- Existing models often assume Markovian behavior, limiting scope.
Purpose of the Study:
- To develop a framework for complete statistical behavior of random walks.
- To analyze the probability of visiting multiple distinct sites at specific times.
- To quantify temporal correlations and non-Markovian properties.
Main Methods:
- Development of a novel theoretical framework.
- Derivation of multiple-time probability distributions.
- Analysis of one-dimensional random walks.
Main Results:
- Demonstrated temporal correlations in random walk site visitation.
- Quantified the non-Markovian nature of these processes.
- Derived new results for the two-time trapping problem.
Conclusions:
- The developed framework provides a comprehensive statistical description of random walks.
- Temporal correlations are inherent in random walk visitation statistics.
- The findings offer insights into the run-and-tumble particle and biased random walk.
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