相关论文: Intermittent Cauchy walks enable optimal 3D search…

L\'{e}vy walks are a particular type of continuous-time random walks which results in a super-diffusive spreading of an initially localized packet. The original one-dimensional model has a simple schematization that is based on starting a…

Using Monte Carlo simulations we examine the diffusive properties of the greedy algorithm in the d-dimensional traveling salesman problem. Our results show that for d=3 and 4 the average squared distance from the origin <r^2> is…

The recurrence features of persistent random walks built from variable length Markov chains are investigated. We observe that these stochastic processes can be seen as L{\'e}vy walks for which the persistence times depend on some internal…

Recent works have explored the properties of L\'evy flights with resetting in one-dimensional domains and have reported the existence of phase transitions in the phase space of parameters which minimizes the Mean First Passage Time (MFPT)…

We study percolation on the sites of a finite lattice visited by a generalized random walk of finite length with periodic boundary conditions. More precisely, consider Levy flights and walks with finite jumps of length $>1$ (like knight's…

We consider a broad class of Continuous Time Random Walks with large fluctuations effects in space and time distributions: a random walk with trapping, describing subdiffusion in disordered and glassy materials, and a L\'evy walk process,…

L\'evy flights and L\'evy walks serve as two paradigms of random walks resembling common features but also bearing fundamental differences. One of the main dissimilarities are discontinuity versus continuity of their trajectories and…

We geometrically analyze the problem of estimating parameters related to the shape and size of a two-dimensional target object on the plane by using randomly distributed distance sensors whose locations are unknown. Based on the analysis…

L\'evy-type walks with correlated jumps, induced by the topology of the medium, are studied on a class of one-dimensional deterministic graphs built from generalized Cantor and Smith-Volterra-Cantor sets. The particle performs a standard…

We present a simple paradigm for detection of an immobile target by a space-time coupled random walker with a finite lifetime. The motion of the walker is characterized by linear displacements at a fixed speed and exponentially distributed…

A continuous Markovian model for truncated Levy random walks is proposed. It generalizes the approach developed previously by Lubashevsky et al. Phys. Rev. E 79, 011110 (2009); 80, 031148 (2009), Eur. Phys. J. B 78, 207 (2010) allowing for…

A combined dynamics consisting of Brownian motion and L\'evy flights is exhibited by a variety of biological systems performing search processes. Assessing the search reliability of ever locating the target and the search efficiency of…

In recent years, mobility models have been reconsidered based on findings by analyzing some big datasets collected by GPS sensors, cellphone call records, and Geotagging. To understand the fundamental statistical properties of the frequency…

We compute the average shape of trajectories of some one--dimensional stochastic processes x(t) in the (t,x) plane during an excursion, i.e. between two successive returns to a reference value, finding that it obeys a scaling form. For…

This paper investigates L\'evy walks with random velocities, extending classical models beyond constant speed assumptions. We derive scaling limits, demonstrating that diffusion depends on interplay between heavy-tailed duration and…

We consider the time evolution of two-dimensional Levy flights in a finite area with periodic boundary conditions. From simulations we show that the fractal path dimension d_f and thus the degree of area coverage grows in time until it…

Recent analysis of empirical data [F. Radicchi, A. Baronchelli & L.A.N. Amaral. PloS ONE 7, e029910 (2012)] showed that humans adopt L\'evy flight strategies when exploring the bid space in on-line auctions. A game theoretical model proved…

A random search is a stochastic process representing the random motion of a particle (denoted as the searcher) that is terminated when it reaches (detects) a target particle or area the first time. In intermittent search the random motion…

We study analytically an intermittent search process in one dimension. There is an immobile target at the origin and a searcher undergoes a discrete time jump process starting at $x_0\geq0$, where successive jumps are drawn independently…

The L\'evy walk process for the lower interval of the time of flight distribution ($\alpha<1$) and with finite resting time between consecutive flights is discussed. The motion is restricted to a region bounded by two absorbing barriers and…