# Dresden 2020 – wissenschaftliches Programm

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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: Hauptvortrag

### Mittwoch, 18. März 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)