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

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 ∼N/N^{λ}, where N is the system size and λ is a tunable parameter that characterizes the process. The survival time distribution has the form P_{N}(τ)∼N^{-θ}J(τ/N^{θ}), where J is a universal scaling function and θ=1-λ. 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 a drifted random walk with Cauchy distributed jumps.