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Full-record statistics of one-dimensional random walks
Léo Régnier1, Maxim Dolgushev1, Olivier Bénichou1
1<a href="https://ror.org/04zaaa143">Laboratoire de Physique Théorique de la Matière Condensée</a>, CNRS, Sorbonne University, 4 Place Jussieu, 75005 Paris, France.
Physical Review. E
|July 18, 2024
Summary
This study introduces a new framework to analyze record statistics and dynamics in stochastic processes. It provides general expressions for key observables, enhancing the understanding of random phenomena.
Area of Science:
- Statistical Physics
- Stochastic Processes
- Probability Theory
Background:
- Record dynamics are fundamental in analyzing sequential data and random processes.
- Existing methods often lack a unified framework for comprehensive statistical analysis.
- Understanding record statistics is crucial for diverse fields, from finance to physics.
Purpose of the Study:
- To develop a comprehensive analytical framework for full-record statistics.
- To derive general expressions for observables related to record dynamics.
- To apply the formalism to various complex stochastic processes.
Main Methods:
- Development of a multiple-time distribution formalism.
- Derivation of general expressions for conditional observables.
- Application to biased random walks, run-and-tumble dynamics, and stochastic resetting.
Main Results:
- A unified framework for analyzing record counts, attainment times, and inter-record intervals.
- General expressions for conditional number of records and conditional time to reach records.
- Demonstration of the framework's applicability across diverse stochastic models.
Conclusions:
- The developed framework offers a powerful tool for studying record dynamics in stochastic processes.
- Provides deeper insights into the statistical properties of sequential random events.
- Applicable to a wide range of physical and mathematical systems exhibiting record-breaking behavior.
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