Previously we have put forward that the sluggish convergence of truncated Lévy flights to a Gaussian (Phys. Rev. Lett. 73 (1994) 2946) together with the scaling power laws in their probability of return to the origin (Nature 376 (1995) 46) can be explained by autocorrelation in data (Physica A...

We develop a scale-invariant truncated Lévy (STL) process to describe physical systems characterized by correlated stochastic variables. The STL process exhibits Lévy stability for the probability density, and hence shows scaling properties (as observed in empirical data); it has the advantage...

The paper is devoted to the relationship between the continuous Markovian description of Lévy flights developed previously (see, e.g., I.A. Lubashevsky, Truncated Lévy flights and generalized Cauchy processes, Eur. Phys. J. B 82 (2011) 189–195 and references therein) and their equivalent...

The statistics of the eigenvalues of symmetric random matrices, composed by real and statistically independent elements following the distribution that maximizes Tsallis's entropy, is carried numerically in the limit of large matrices. For entropic indexes in the interval −∞<q<53, by using a convenient rescale of variables, it is possible to show that such matrices fall in the same class of the Gaussian orthogonal ensemble (GOE). For the entropic index 53⩽q<3, the density of eigenvalues and the distribution of level spacings do not seem to follow a simple rescale of variables involving different values of q, and exhibit a behavior very distinct from the GOE: both quantities present long tails for 53⩽q⩽2, and such long tails die out when q>2. The density of...</q<53,>

Since real processes seem to departure from standard Lévy distributions, modifications to the latter have been suggested in literature. These include (abruptly) truncated (Phys. Rev. Lett. 73 (1994) 2946), smoothly truncated (Phys. Rev. E 52 (1995) 1197; Phys. Lett. A 266 (2000) 282) and gradually...

The directional motion of a particle in an unbound potential in the presence of either non-Ohmic memory friction or Lévy flight is considered. Time-dependent probability passing over the saddle point of a parabolic potential is derived exactly. The results show that the Lévy flights break...

There has been growing interest in the study of Lévy flights observed in the movements of biological organisms performing random walks while searching for other organisms. Here, we approach the problem of what is the best statistical strategy for optimizing the encounter rate between...

We study the long time asymptotics of probability density functions (pdfs) of Lévy flights in confining potentials that originate from inhomogeneities of the environment in which the flights take place. To this end we employ two model patterns of dynamical behavior: Langevin-driven and...

One of several critical issues in the development of optimal disease containment and eradication strategies is the knowledge of underlying contacts between individuals. Here we employ random search strategies to identify all possible links, representing direct or indirect interactions between...