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DY: Fachverband Dynamik und Statistische Physik

DY 59: Brownian Motion and Anomalous Diffusion

DY 59.10: Talk

Friday, March 22, 2024, 12:00–12:15, BH-N 334

Concentration-of-measure in time-average statistical mechanics — •Rick Bebon and Aljaz Godec — Max Planck Institute for Multidisciplinary Sciences, Göttingen, Germany

Nowadays, state-of-the-art single-molecule or particle-tracking experiments provide direct access to path-dependent observables by probing individual trajectories. Obtained by means of time-averaging a limited number of individual realizations each with a finite duration, inferred estimates are typically afflicted by large systematic uncertainties, making a correct interpretation a priori non-trivial. Recent theoretical advances motivate a deeper understanding of fluctuating path-observables, as the latter would allow for decoding important and otherwise hidden information about the underlying microscopic dynamics. Reliably interpreting sample-to-sample fluctuations of time-averaged functionals of noisy trajectories therefore remains a crucial but challenging task, especially in the presence of subsampling. Instigated by these difficulties, we propose a non-asymptotic concentration-of-measure perspective on functionals of overdamped Langevin dynamics that allows a general and correct rationalization of time-averaged observables and their fluctuations for arbitrary times. Subsequently, we demonstrate how bounding the probability that an individual realization deviates from the mean value by more than any fixed amount provides a new outlook on time-averaged observables.

Keywords: Langevin dynamics; Brownian functionals; non-equilibrium statistical mechanics; single-molecule experiments; uncertainty quantification