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Animal behavior is shaped by a myriad of mechanisms acting on a wide range of scales, which hampers quantitative reasoning and the identification of general principles. Here, we combine data analysis and theory to investigate the…

In this paper we discuss the problem of the estimation of extreme event occurrence probability for data drawn from some multifractal process. We also study the heavy (power-law) tail behavior of probability density function associated with…

In random systems consisting of grains with size distributions the transport properties are difficult to explore by network models. However, the concentration dependence of effective conductivity and its critical properties can be…

Understanding transport processes in complex nanoscale systems, like ionic conductivities in nanofluidic devices or heat conduction in low dimensional solids, poses the problem of examining fluctuations of currents within nonequilibrium…

Multifractal properties of a tracer density passively advected by a compressible random velocity field are characterized. A relationship is established between the statistical properties of mass on the dynamical fractal attractor towards…

In this paper we introduce and study several multivariate, heavy-tailed distribution classes, and we explore their closure properties and their applications. We consider the class of multivariate, positively decreasing distributions, and…

This article gives a comprehensive description of the fractal geometry of conformally-invariant (CI) scaling curves, in the plane or half-plane. It focuses on deriving critical exponents associated with interacting random paths, by…

We consider self-avoiding walk on finite graphs with large girth. We study a few aspects of the model originally considered by Lawler, Schramm and Werner on finite balls in Z^d. The expected length of a random self avoiding path is…

In this paper we introduce a general framework for the study of limits of relational structures in general and graphs in particular, which is based on a combination of model theory and (functional) analysis. We show how the various…

Branching random walks on multidimensional lattice with heavy tails and a constant branching rate are considered. It is shown that under these conditions (heavy tails and constant rate), the front propagates exponentially fast, but the…

Modeling of phenomena such as anomalous transport via fractional-order differential equations has been established as an effective alternative to partial differential equations, due to the inherent ability to describe large-scale behavior…

Consider d uniformly random permutation matrices on n labels. Consider the sum of these matrices along with their transposes. The total can be interpreted as the adjacency matrix of a random regular graph of degree 2d on n vertices. We…

We extend Feynman's analysis of an infinite ladder circuit to fractal circuits, providing examples in which fractal circuits constructed with purely imaginary impedances can have characteristic impedances with positive real part. Using…

We consider a basic one-dimensional model of diffusion which allows to obtain a diversity of diffusive regimes whose speed depends on the moments of the per-site trapping time. This model is closely related to the continuous time random…

We show that the generalized diffusion coefficient of a subdiffusive intermittent map is a fractal function of control parameters. A modified continuous time random walk theory yields its coarse functional form and correctly describes a…

This study in centered on models accounting for stochastic deformations of sample paths of random walks, embedded either in $\mathbb{Z}^2$ or in $\mathbb{Z}^3$. These models are immersed in multi-type particle systems with exclusion.…

Social, technological and economic time series are divided by events which are usually assumed to be random albeit with some hierarchical structure. It is well known that the interevent statistics observed in these contexts differs from the…

In this article we show the relationship between the Pareto distribution and the gamma distribution. This shows that the second one, appropriately extended, explains some anomalies that arise in the practical use of extreme value theory.…

We show that a simple mechanistic model of spatial dispersal for settling organisms, subject to parameter variability, can generate heavy-tailed radial probability density functions. The movement of organisms in the model consists of a…

We consider the fitting of heavy tailed data and distribution with a special attention to distributions with a non--standard shape in the "body" of the distribution. To this end we consider a dense class of heavy tailed distributions…