相关论文: Target search kinetics for random walkers with mem…
We present a random walk model that exhibits asymptotic subdiffusive, diffusive, and superdiffusive behavior in different parameter regimes. This appears to be the first instance of a single random walk model leading to all three forms of…
The first-passage-time problem for a Brownian motion with alternating infinitesimal moments through a constant boundary is considered under the assumption that the time intervals between consecutive changes of these moments are described by…
During a random search, resetting the searcher's position from time to time to the starting point often reduces the mean completion time of the process. Although many different resetting models have been studied over the past ten years,…
Persistence, defined as the probability that a fluctuating signal has not reached a threshold up to a given observation time, plays a crucial role in the theory of random processes. It quantifies the kinetics of processes as varied as phase…
Active particles, which are self-propelled nonequilibrium systems, are modelled by overdamped Langevin equations with colored noise, emulating the self-propulsion. In this chapter, we present a review of the theoretical results for the…
The problem of the detection statistics of a quantum walker has received increasing interest, connected as it is to the problem of quantum search. We investigate the effect of employing a moving detector, using a projective measurement…
First passage phenomena arise across physics, biology, and finance when stochastic processes first reach a threshold, triggering downstream events. Examples include the irreversible exit from a domain, a biochemical reaction, a financial…
We consider a Brownian particle diffusing in a one dimensional interval with absorbing end points. We study the ramifications when such motion is interrupted and restarted from the same initial configuration. We provide a comprehensive…
We determine the full distribution and moments of the first passage time for a wide class of stochastic search processes in the limit of frequent stochastic resetting. Our results apply to any system whose short-time behavior of the search…
We introduce a non-equilibrium discrete-time random walk model on multiplex networks, in which at each time step the walker first undergoes a random jump between neighboring nodes in the same layer, and then tries to hop from one node to…
Non-Markovian quantum effects are typically observed in systems interacting with structured reservoirs. Discrete-time quantum walks are prime example of such systems in which, quantum memory arises due to the controlled interaction between…
Given a discrete-time non-lattice supercritical branching random walk in $\mathbb{R}^d$, we investigate its first passage time to a shifted unit ball of a distance $x$ from the origin, conditioned upon survival. We provide precise…
Very recently, a fundamental observable has been introduced and analyzed to quantify the exploration of random walks: the time $\tau_k$ required for a random walk to find a site that it never visited previously, when the walk has already…
We design a method to optimize the global mean first-passage time (GMFPT) of multiple random walkers searching in complex networks for a general target, without specifying the property of the target node. According to the Laplace…
Autonomous robots are commonly tasked with the problem of area exploration and search for certain targets or artifacts of interest to be tracked. Traditionally, the problem formulation considered is that of complete search and thus -…
Applications of first passage times in stochastic processes arise across a wide range of length and time scales in biological settings. After an initial technical overview, we survey representative applications and their corresponding…
We consider random search processes alternating stochastically between diffusion and ballistic motion, in which the distribution function of ballistic motion directions varies from point to point in space. The specific space dependence of…
The first hitting times of a stochastic process, i.e., the first time a process reaches a particular level, are of significant interest across various scientific disciplines, including biology, chemistry, and economics. We modify the…
The first passage is a generic concept for quantifying when a random quantity such as the position of a diffusing molecule or the value of a stock crosses a preset threshold (target) for the first time. The last decade saw an enlightening…
We present a model for a random walk with memory, phenomenologically inspired in a biological system. The walker has the capacity to remember the time of the last visit to each site and the step taken from there. This memory affects the…