Related papers: First passage under restart with branching
First-passage processes can be divided in two classes: those that are accelerated by the introduction of restart and those that display an opposite response. In physical systems, a transition between the two classes may occur as governing…
We consider a random walker on a ring, subjected to resetting at Poisson-distributed times to the initial position (the walker takes the shortest path along the ring to the initial position at resetting times). In the case of a Brownian…
Fluctuations in stochastic systems are usually characterized by the full counting statistics, which analyzes the distribution of the number of events taking place in the fixed time interval. In an alternative approach, the distribution of…
We show that the transience or recurrence of a random walk in certain random environments on an arbitrary infinite locally finite tree is determined by the branching number of the tree, which is a measure of the average number of branches…
The mean completion time of a stochastic process may be rendered finite and minimised by a judiciously chosen restart protocol, which may either be stochastic or deterministic. Here we study analytically an arbitrary stochastic search…
Optimization of a random processes by restart is a subject of active theoretical research in statistical physics and has long found practical application in computer science. Meanwhile, one of the key issues remains largely unsolved: when…
The first-passage time is proposed as an independent thermodynamic parameter of the statistical distribution that generalizes the Gibbs distribution. The theory does not include the determination of the first passage statistics itself. A…
We consider the problem of bounding mean first passage times for a class of continuous-time Markov chains that captures stochastic interactions between groups of identical agents. The quantitative analysis of such probabilistic population…
Classical first passage under resetting is a paradigm in the search process. Despite its multitude of applications across interdisciplinary sciences, experimental realizations of such resetting processes posit practical challenges in…
We study the effect of restart, and retry, on the mean completion time of a generic process. The need to do so arises in various branches of the sciences and we show that it can naturally be addressed by taking advantage of the classical…
First passage time statistics in disordered systems exhibiting scale invariance are studied widely. In particular, long trapping times in energy or entropic traps are fat-tailed distributed, which slow the overall transport process. We…
Resetting a stochastic process has been shown to expedite the completion time of some complex tasks, such as finding a target for the first time. Here we consider the cost of resetting by associating to each reset a cost, which is a…
We revisit the simple lattice random walk (P\'{o}lya walk) and the Sisyphus random walk in $\mathbb{Z}$, in the presence of random restarts. We use a relatively direct approach namely First passage under restart for discrete space and time…
First passage percolation with recovery is a process aimed at modeling the spread of epidemics. On a graph $G$ place a red particle at a reference vertex $o$ and colorless particles (seeds) at all other vertices. The red particle starts…
These notes are based on the lectures that I gave (virtually) at the Bruneck Summer School in 2021 on first-passage processes and some applications of the basic theory. I begin by defining what is a first-passage process and presenting the…
Aging, the dependence of the dynamics of a physical process on the time $t_a$ since its original preparation, is observed in systems ranging from the motion of charge carriers in amorphous semiconductors over the blinking dynamics of…
Interesting theoretical problems of target search or threshold crossing, formally known as {\it first passage}, often arise in both diffusive transport problems as well as problems of chemical reaction kinetics. We study three systems…
The study of first passage times for diffusing particles reaching target states is foundational in various practical applications, including diffusion-controlled reactions. In this work, we present a bi-scaling theory for the probability…
We prove non-universality results for first-passage percolation on the configuration model with i.i.d. degrees having infinite variance. We focus on the weight of the optimal path between two uniform vertices. Depending on the properties of…
By periodically returning a search process to a known or random state, random resetting possesses the potential to unveil new trajectories, sidestep potential obstacles, and consequently enhance the efficiency of locating desired targets.…