TY - JOUR A1 - Teomy, Eial A1 - Roichman, Yael A1 - Shokef, Yair T1 - Multiple peaks in the displacement distribution of active random walkers JF - Journal of statistical mechanics: theory and experiment N2 - We consider a simple model for active random walk with general temporal correlations, and investigate the shape of the probability distribution function of the displacement during a short time interval. We find that under certain conditions the distribution exhibits multiple peaks and we show analytically and numerically that the existence of these peaks is governed by the walker?s tendency to move forward, while the correlations between the timing of its active motion control the magnitude and shape of the peaks. In particular, we find that in a homogeneous system such peaks can occur only if the persistence is strong enough. KW - 16 KW - 4 Y1 - 2019 U6 - https://doi.org/10.1088/1742-5468/ab4fde SN - 1742-5468 VL - 2019 IS - 11 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Metzler, Ralf T1 - Brownian motion and beyond: first-passage, power spectrum, non-Gaussianity, and anomalous diffusion JF - Journal of statistical mechanics: theory and experiment N2 - Brownian motion is a ubiquitous physical phenomenon across the sciences. After its discovery by Brown and intensive study since the first half of the 20th century, many different aspects of Brownian motion and stochastic processes in general have been addressed in Statistical Physics. In particular, there now exists a very large range of applications of stochastic processes in various disciplines. Here we provide a summary of some of the recent developments in the field of stochastic processes, highlighting both the experimental findings and theoretical frameworks. KW - 15 KW - 4 Y1 - 2019 U6 - https://doi.org/10.1088/1742-5468/ab4988 SN - 1742-5468 VL - 2019 IS - 11 PB - IOP Publ. Ltd. CY - Bristol ER -