SKM 2023 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 6: Statistical Physics: General I
DY 6.7: Vortrag
Montag, 27. März 2023, 11:45–12:00, ZEU 160
Mean first-passage times of continuous-time random walkers determined through Wiener-Hopf integral equations — •Marcus Dahlenburg1,2 and Gianni Pagnini1,3 — 1BCAM-Basque Center for Applied Mathematics, Alameda de Mazarredo 14, 48009 Bilbao, Basque Country, Spain — 2Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam, Germany — 3Ikerbasque-Basque Foundation for Science, Plaza Euskadi 5, 48009 Bilbao, Basque Country, Spain
Asymmetric continuous-time random walks in continuous-space characterised by waiting-times with finite mean and by jump-amplitudes with both finite mean and finite variance are governed by an advection-diffusion equations in the asymptotic limit. The mean first-passage time (MFPT) of such an advective-diffusive system on a halfline results to be finite when the advecting drift is in the direction of the boundary. In our investigation we derive an inhomogeneous Wiener-Hopf integral equation that allows to avoids approximated results in the asymptotic limits and leads indeed to the exact determination of the MFPT. This quantity depends on the average of the waiting-times only but it conserves the information about the whole distribution of the jump-amplitudes. Through the case study of asymmetric double-exponential distributions of the jump-amplitudes one may identifies a length-scale, that defines the transition from starting points near the boundary to starting points far-away from the boundary where the MFPT loses the information about the exact shape of the jump-amplitudes' distribution and only conserves their mean.