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

TL;DR

This paper investigates survival time statistics in a noisy sample space reducing process, revealing scaling behaviors and a universal distribution, and links these findings to record statistics in correlated random events.

Contribution

It introduces a novel connection between noisy SSR processes and record statistics in correlated random series, providing analytical and simulation insights.

Findings

Mean and standard deviation scale as N/N^{λ}

Survival time distribution follows a universal scaling form

Analytical conjecture links SSR survival times to record statistics in correlated series

Abstract

We study survival time statistics in a noisy sample space reducing (SSR) process. Our simulations suggest that both the mean and standard deviation scale as $\sim N/N^{\lambda}$, where $N$ is the system size and $\lambda$ is a tunable parameter that characterizes the process. The survival time distribution has the form $\mathcal{P}_{N}(\tau)\sim N^{-\theta}J(\tau/N^{\theta})$, where $J$ is a universal scaling function and $\theta = 1-\lambda$. Analytical insight is provided by a conjecture for the equivalence between the survival time statistics in the noisy SSR process and the record statistics in a correlated time series modeled as drifted random walk with Cauchy distributed jumps.