Berlin 2024 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 41: Statistical Physics: General

DY 41.10: Vortrag

Donnerstag, 21. März 2024, 12:00–12:15, BH-N 128

Extrapolation of Rate Functions from Finite-Size Numerical Large-Deviation Simulations — •Peter Werner and Alexander K. Hartmann — Institute of Physics, University of Oldenburg, Germany

When performing large-deviation simulations, a typical question is whether the system at hand follows a large-deviation principle [1]. This can be done by checking if the probability distribution of an intensiv system quantity converges for increasing system sizes to a form that possesses a corresponding rate-function. Analytical solutions exist for certain models that allow for comparisons with numerical results [2]. Some special-purpose algorithms, as the cloning approach [3], can be used for a direct estimate. However, by using data from arbitrary simulation procedures, the results usually depend heavily on the specific finite-size scaling behaviour of the probability distributions. Here, a numerical procedure is presented that relies on samples obtained from general biased Monte-Carlo simulations [4]. Instead of working with the probability distributions directly, the scaled cumulant-generating function is approximated. From this approximation the Gärtner-Ellis theorem is applied to obtain the rate function. Example results are shown for a simple binomial distributed variable and the largest connected component in Erdös-Rényi random graphs.

[1] H. Touchette, Phys. Rep. 478, 1-69 (2012)

[2] A. K. Hartmann, Eur. Phys. J. Special Topics 226,567-579 (2017)

[3] E. Hidalgo, JSTAT 2018, 083211 (2018)

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

Keywords: large deviation theory; rate function estimation; computer simulations; random graphs