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The problem of how to estimate diffusion on a graph effectively is of importance both theoretically and practically. In this paper, we make use of two widely studied indices, geodesic distance and mean first-passage time ($MFPT$) for random…
We study the asymptotics of a two-dimensional stochastic differential system with a degenerate diffusion matrix. This system describes the dynamics of a population where individuals contribute to the degradation of their environment through…
Anomalous diffusion phenomena have been observed in many complex physical and biological systems. One significant advance recently is the physical extension of particle's motion in static medium to uniformly (and even nonuniformly)…
We address this work to investigate some statistical properties of symbolic sequences generated by a numerical procedure in which the symbols are repeated following a power law probability density. In this analysis, we consider that the sum…
Anomalous diffusion processes, in particular superdiffusive ones, are known to be efficient strategies for searching and navigation by animals and also in human mobility. One way to create such regimes are L\'evy flights, where the walkers…
We study simple models of intermittency, involving switching between two states, within the dynamical large-deviation formalism. Singularities appear in the formalism when switching is cooperative, or when its basic timescale diverges. In…
We quantify superdiffusive transience for a two-dimensional random walk in which the vertical coordinate is a martingale and the horizontal coordinate has a positive drift that is a polynomial function of the individual coordinates and of…
This study introduces a comparative modeling framework using stationary and non-stationary transition probabilities within a Markov Decision Process (MDP) to assess COVID-19 disease dynamics. Stationary transition probabilities assume…
Consider a chaotic dynamical system generating Brownian motion-like diffusion. Consider a second, non-chaotic system in which all particles localize. Let a particle experience a random combination of both systems by sampling between them in…
We formulate a new model for transport in stochastic media with long-range spatial correlations where exponential attenuation (controlling the propagation part of the transport) becomes power law. Direct transmission over optical distance…
We analyze how the transient dynamics of large dynamical systems in the vicinity of a stationary point, modeled by a set of randomly coupled linear differential equations, depends on the network topology. We characterize the transient…
We have used Dynamic Monte Carlo (DMC) methods and analytical techniques to analyze Single-File Systems for which diffusion is infinitely-fast. We have simplified the Master Equation removing the fast reactions and we have introduced a DMC…
We investigate three different methods for systematically approximating the diffusion coefficient of a deterministic random walk on the line which contains dynamical correlations that change irregularly under parameter variation. Capturing…
Motion of particles in many systems exhibits a mixture between periods of random diffusive like events and ballistic like motion. In many cases, such systems exhibit strong anomalous diffusion, where low order moments $< |x(t)|^q >$ with…
We investigate dissipative dynamical systems under the influence of an external driving with two or more frequencies. Our main quantities of interest are long-time averages of expectation values which turn out to exhibit universal features.…
We consider chains of one-dimensional, piecewise linear, chaotic maps with uniform slope. We study the diffusive behaviour of an initially nonuniform distribution of points as a function of the slope of the map by solving Frobenius-Perron…
We introduce a novel random walk model that emerges in the event-chain Monte Carlo (ECMC) of spin systems. In the ECMC, the lifting variable specifying the spin to be updated changes its value to one of its interacting neighbor spins. This…
We use a one-dimensional random walk on $D$-dimensional hyper-spheres to determine the critical behavior of statistical systems in hyper-spherical geometries. First, we demonstrate the properties of such walk by studying the phase diagram…
Chemical master equation plays an important role to describe the time evolution of homogeneous chemical system. In addition to the reaction process, it is also accompanied by physical diffusion of the reactants in complex system that is…
We study systems of globally coupled interval maps, where the identical individual maps have two expanding, fractional linear, onto branches, and where the coupling is introduced via a parameter - common to all individual maps - that…