Related papers: Random walks with stochastic resetting in complex …
In this work, we propose a scheme that provides an analytical estimate for the time-dependent degree distribution of some networks. This scheme maps the problem into a random walk in degree space, and then we choose the paths that are…
A powerful strategy to accelerate quantum-walk-based search algorithms leverages on resetting protocols, where a detector monitors a target site and the evolution of the walker is restarted if no detection occurs within a fixed time…
Self-interacting random walks (SIRWs) show long-range memory effects that result from the interaction of the random walker at time $t$ with the territory already visited at earlier times $t'<t$. This class of non-Markovian random walks has…
The rotor walk is a derandomized version of the random walk on a graph. On successive visits to any given vertex, the walker is routed to each of the neighboring vertices in some fixed cyclic order, rather than to a random sequence of…
In this paper, we propose a general framework for the trapping problem on a weighted network with a perfect trap fixed at an arbitrary node. By utilizing the spectral graph theory, we provide an exact formula for mean first-passage time…
We give a complete and unified description -- under some stability assumptions -- of the functional scaling limits associated with some persistent random walks for which the recurrent or transient type is studied in [1]. As a result, we…
Recently the so-called Prabhakar generalization of the fractional Poisson counting process attracted much interest for his flexibility to adapt real world situations. In this renewal process the waiting times between events are IID…
Random walks are a fundamental tool for analyzing realistic complex networked systems and implementing randomized algorithms to solve diverse problems such as searching and sampling. For many real applications, their actual effect and…
Sood and Grassberger studied in [Phys. Rev. Lett. 99, 098701 (2007)] random walks on random graphs that are biased towards a fixed target point. They put forward a critical bias strength b_c such that a random walker on an infinite graph…
Many biological, social, and communication systems can be modeled by ``searchers'' moving through a complex network. For example, intracellular cargo is transported on tubular networks, news and rumors spread through online social networks,…
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…
Monte Carlo (MC) simulations of transport in random porous networks indicate that for high variances of the log-normal permeability distribution, the transport of a passive tracer is non-Fickian. Here we model this non-Fickian dispersion in…
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…
Performing random walks in networks is a fundamental primitive that has found applications in many areas of computer science, including distributed computing. In this paper, we focus on the problem of sampling random walks efficiently in 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…
We study a discrete-time quantum walk in presence of a detector at $x_D$ initially. The detector here is repeatedly removed after a span of $t_R$, the removal time, and reinserted at random locations. Two relocation rules are considered…
We solve an adaptive search model where a random walker or L\'evy flight stochastically resets to previously visited sites on a $d$-dimensional lattice containing one trapping site. Due to reinforcement, a phase transition occurs when the…
Renewal processes are zero-dimensional processes defined by independent intervals of time between zero crossings of a random walker. We subject renewal processes them to stochastic resetting by setting the position of the random walker to…
We study Markov chains on a lattice in a codimension-one stratified independent random environment, exploiting results established in [2]. First of all the random walk is transient in dimension at least three. Focusing on dimension two,…
In 2008, T\'oth and Vet\H{o} defined the self-repelling random walk with directed edges as a non-Markovian random walk on $\mathbb{Z}$: in this model, the probability that the walk moves from a point of $\mathbb{Z}$ to a given neighbor…