The Montroll-Weiss continuous time random walk has found numerous applications due its ease of use and ability to describe both regular and anomalous diffusion. Yet, despite its broad applicability and generality, the model cannot account for effects coming from random diffusivity fluctuations, which have been observed in the motion of asset prices and molecules. To bridge this gap, we introduce a doubly stochastic version of the model in which waiting times between jumps are replaced with a fluctuating jump rate. 

Motivated by recent experiments, a stylized model for a random walk that interacts with its environment is developed. The model is used to show that even a limited ability of a tracer to push away obstacles that block its path will always lead to caging and thus to the loss of the percolation transition—a hallmark of random walks in disorder media.

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We combine stochastic resetting with Metadynamics and show that this can accelerate molecular dynamics simulations beyond either method separately. We also show that applying stochastic resetting can be an alternative to the challenging task of finding optimal collective variables for Metadynamics, at almost no additional computational cost. Finally, we propose a method to extract unbiased mean first-passage times from Metadynamics simulations with resetting, resulting in an improved tradeoff between speedup and accuracy. 

First-passage times provide invaluable insight into fundamental properties of stochastic processes. Yet, various forms of gating mask first-passage times and differentiate them from actual detection times. We develop a universal—model free—framework for the inference of first-passage times from the detection times of gated first-passage processes. The approach opens a peephole into a myriad of systems whose direct observation is limited because of their underlying physics or imperfect observation conditions.

How much time does it take for a sticky particle to diffuse out of a given compartment? We develop an analytical framework to solve this open problem, which has applications in biophysics and nanoscience. We present the first exact solution to the problem, revealing that adsorption and desorption rates (which are largely unknown) can be inferred from the mean and variance of the escape time. An efficient scheme for simulating “sticky escape” from arbitrary domains is also presented.

The macroscopic theory of adsorption dates back more than a century and is now well-established. Yet, despite recent advancements, a detailed and self-contained theory of single-particle adsorption is still lacking. Here, we bridge this gap by developing a microscopic theory of adsorption kinetics, from which the macroscopic properties follow directly. One of our central achievements is the derivation of a microscopic version of the seminal Ward–Tordai relation, and its generalization to arbitrary dimension, geometry, and initial conditions.