Dresden 2020 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 40: Data Analytics, Extreme Events, and Nonlinear Stochastic Systems (joint session DY/SOE)

DY 40.1: Invited Talk

Wednesday, March 18, 2020, 15:00–15:30, ZEU 118

I want it all and I want it now! — •Alexander K. Hartmann — University of Oldenburg, Germany

For every random process, all measurable quantities are described comprehensively through their probability distributions. Ideally, they would be obtained analytically, i.e., completely. Since most physical models are not accessible analytically, one has to perform numerical simulations. Usually this means one does many independent runs, allowing one to measure histograms. Since the number of repetitions is limited, maybe 10 million, correspondingly the distributions can be estimated in a range down to probabilities like 10⁻¹⁰. But what if one wants to obtain the full distribution, in the spirit of obtaining all information? Thus, one desires to get the distribution down to the rare events, without waiting for a huge running time.

Here, we study rare events using a very general black-box method [1]. It is based on sampling vectors of random numbers within an artificial finite-temperature (Boltzmann) ensemble to access rare events and large deviations for almost arbitrary equilibrium and non-equilibrium processes. In this way, we obtain probabilities as small as 10⁻⁵⁰⁰ and smaller, hence (almost) the full distribution can be obtained in a reasonable amount of time. Examples are presented for applications to random graphs [2], traffic flow models, biological sequence alignment, particle diffusion, or calculation of partition functions [3].

[1] A.K. Hartmann, Phys. Rev. E 89, 052103 (2014)

[2] A.K. Hartmann and M. Mézard, Phys. Rev. E 97, 032128 (2018)

[3] A.K. Hartmann, Phys. Rev. Lett. 94, 050601 (2005)