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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Restart has the potential of expediting or impeding the completion times of general random processes. Consequently, the issue of mean-performance takes center stage: quantifying how the application of restart on a process of interest impacts its completion-time's mean. Going beyond the mean, little is known on how restart affects stochasticity measures of the completion time. We present a comprehensive analysis that quantifies how sharp restart—a keystone restart protocol—impacts the the entropy and diversity of the completion time.

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.

We present a method for enhanced sampling of molecular dynamics simulations using stochastic resetting. We employ resetting for enhanced sampling of molecular simulations for the first time, and show that it accelerates long time scale processes by up to an order of magnitude in examples ranging from simple models to a molecular system. Most importantly, we recover the mean transition time without resetting, which is typically too long to be sampled directly, from accelerated simulations at a single restart rate.

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.

We generalize the model of diffusion with resetting to account for situations where a particle is returned only a fraction of its distance to the origin, e.g., half way. We show that this model always attains a steady-state distribution which can be written as an infinite sum of independent, but not identical, Laplace random variables. As a result, we find that the steady-state transitions from the known Laplace form which is obtained in the limit of full resetting to a Gaussian form which is obtained close to the limit of no resetting.