Related papers: Target search kinetics for random walkers with mem…
Agents searching for a target can improve their efficiency by memorizing where they have already been searching or by cooperating with other searchers and using strategies that benefit from collective effects. This chapter reviews such…
The statistics of first-passage times of random walks to target sites has proved to play a key role in determining the kinetics of space exploration in various contexts. In parallel, the number of distinct sites visited by a random walker…
First passage time plays a fundamental role in dynamical characterization of stochastic processes. Crucially, our current understanding on the problem is almost entirely relies on the theoretical formulations, which assume the processes…
The first-passage time (FPT), defined as the time a random walker takes to reach a target point in a confining domain, is a key quantity in the theory of stochastic processes. Its importance comes from its crucial role to quantify the…
We consider a minimal model of persistent random searcher with short range memory. We calculate exactly for such searcher the mean first-passage time to a target in a bounded domain and find that it admits a non trivial minimum as function…
In this paper we present a computation of the mean first-passage times both for a random walk in a discrete bounded lattice, between a starting site and a target site, and for a Brownian motion in a bounded domain, where the target is a…
In this paper we study some aspects of search for an immobile target by a swarm of N non-communicating, randomly moving searchers (numbered by the index k, k = 1, 2,..., N), which all start their random motion simultaneously at the same…
The presence of temporal correlations in random movement trajectories is a widespread phenomenon across biological, chemical and physical systems. The ubiquity of persistent and anti-persistent motion in many natural and synthetic systems…
Finding a target in a complex environment is a fundamental challenge in nature, from chemical reactions to sperm reaching an egg. An effective strategy to reduce the time needed to reach a target is to deploy many searchers, increasing the…
First-passage properties are central to the kinetics of target-search processes. Theoretical approaches so far primarily focused on predicting first-passage statistics for a given process or model. In practice, however, one faces the…
We review some representative results for first-passage problems involving so-called mortal or evanescent walkers, i.e., walkers with a finite lifetime. The mortality constraint plays a key role in the modeling of many real scenarios, as it…
Stochastic search processes are ubiquitous in nature and are expected to become more efficient when equipped with a memory, where the searcher has been before. A natural realization of a search process with long-lasting memory is a…
Self-interacting random walks are endowed with long range memory effects that emerge from the interaction of the random walker at time $t$ with the territory that it has visited at earlier times $t'<t$. This class of non Markovian random…
The first passage search of a diffusing target (prey) by multiple searchers (predators) in confinement is an important problem in the stochastic process literature. While the analogous problem in open space has been studied in some details,…
How much time does it take for a fluctuating system, such as a polymer chain, to reach a target configuration that is rarely visited -- typically because of a high energy cost ? This question generally amounts to the determination of the…
We analyze a one-dimensional intermittent random walk on an unbounded domain in the presence of stochastic resetting. In this process, the walker alternates between local intensive search, diffusion, and rapid ballistic relocations in which…
This thesis explores a central question: how does memory affect the way random walkers explore space? By analyzing various non-Markovian models, where past behavior directly influences future dynamics, we uncover new mechanisms and…
We introduce a general approach for the study of the collective dynamics of non-interacting random walkers on connected networks. We analyze the movement of $R$ independent (Markovian) walkers, each defined by its own transition matrix. By…
We investigate the role of stochastic resetting in non-Markovian systems, where memory effects arise due to slow relaxation, rugged energy landscapes, disordered environments, and molecular crowding. Using the celebrated continuous-time…
We present a novel computational method of first-passage times between a starting site and a target site of regular bounded lattices. We derive accurate expressions for all the moments of this first-passage time, validated by numerical…