Correspondence between a noisy sample-space-reducing process and records in correlated random events

Area of Science:

• Statistical Physics
• Complex Systems Analysis
• Stochastic Processes

Background:

• Understanding system dynamics and survival probabilities is crucial in various scientific fields.
• Noisy sample-space-reducing (SSR) processes present unique challenges in statistical analysis.
• Characterizing the behavior of such systems requires advanced simulation and analytical techniques.

Purpose of the Study:

• To investigate the survival time statistics in a noisy sample-space-reducing (SSR) process.
• To identify universal scaling laws governing survival times.
• To establish a connection between SSR processes and time series analysis.

Main Methods:

• Computational simulations were employed to model the noisy SSR process.
• Statistical analysis was performed on simulated survival time data.
• A theoretical conjecture was formulated to link SSR statistics with record statistics of drifted random walks.

Main Results:

• Both the mean and standard deviation of survival times exhibit scaling behavior proportional to N/N^{λ}.
• The survival time distribution follows a universal form P_{N}(τ)∼N^{-θ}J(τ/N^{θ}), with θ=1-λ.
• Simulations suggest an equivalence between SSR survival statistics and record statistics in correlated time series.

Conclusions:

• The study reveals universal scaling laws for survival times in noisy SSR processes.
• A connection is proposed between the statistical properties of SSR systems and correlated time series.
• The findings provide a framework for analyzing complex systems exhibiting sample space reduction.