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DY: Fachverband Dynamik und Statistische Physik
DY 31: Poster: Statistical Physics
DY 31.5: Poster
Wednesday, March 20, 2024, 15:00–18:00, Poster C
Controlling Uncertainty of Empirical First-Passage Times in the Small-Sample Regime — •Rick Bebon and Aljaz Godec — Max Planck Institute for Multidisciplinary Sciences, Göttingen, Germany
Central to the kinetics of target-search processes, first-passage phenomena find successful applications across virtually all scientific domains. Here, we address the challenge of controlling uncertainty of empirical first-passage times τn≡∑i=1n τi/n, i.e., the sample-mean inferred from under-sampled experimental or simulation data. Understanding the ramifications of the small-sample regime, such as non-Gaussian fluctuations, is crucial for obtaining trustworthy estimates but yet remains a daunting task not amenable to standard error-analysis techniques. Consequently, we outline a non-asymptotic theory that enables robust error control in empirical first-passage times of reversible Markov processes regardless of sample-size under minimal assumptions. Key results include concentration inequalities that bound deviations of the sample-mean from the true mean first-passage time from above and sharp two-sided bounds on the expected maximum and minimum deviation from the mean in any given sample.
Keywords: first-passage; stochastic processes; uncertainty quantification; statistical inference; extreme value statistics