Dresden 2020 – scientific programme
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SOE: Fachverband Physik sozio-ökonomischer Systeme
SOE 10: Data Analytics, Extreme Events, Nonlinear Stochastic Systems, and Networks (joint session DY/SOE)
SOE 10.5: Talk
Wednesday, March 18, 2020, 16:30–16:45, ZEU 118
Large-deviation simulation of height distribution for the KPZ equation: dependence on initial conditions and morphologie of extreme configurations — •Alexander K. Hartmann1, Pierre Le Doussal2, Alexandre Krajenbrink2, Baruch Meerson3, and Pavel Sasorov4 — 1University of Oldenburg, Germany — 2Ecole Normale Supérieure, Paris, France — 3Hebrew University of Jerusalem, Israel — 4Keldysh Institute of Applied Mathematics, Moscow, Russia
The distribution of relative free energies H of directed polymers in disordered media is studied, which is in the KPZ universality class. We study the distribution at large temperatures, corresponding to short times in KPZ. Using a statistical mechanics-based large-deviation approach, the distribution can be obtained over a large range of the support, down to a probability density as small as 10−1000 [1]. We compare with analytical predictions for different types of initial conditions and for full as well as for half space [2]. A very good agreement is found for H<0 and a strong convergence is visible for H>0. Furthermore, we study the morphology of atypical fluctuations [3], compare with analytical results from the optimal fluctuation method, and find again a good agreement.
[1] A.K. Hartmann, P. Le Doussal, S.N. Majumdar, A. Rosso and G. Schehr, Europhys. Lett. 121, 67004 (2018).
[2] A.K. Hartmann, A. Krajenbrink, and P. Le Doussal, preprint arXiv:1909.0384.
[2] A.K. Hartmann, B. Meerson, and P. Sasorov, arXiv: 1907.05677.