Ricerc@Sapienza

We consider two random walkers embedded in a finite, two-dimension comb and we study the mean first-encounter time (MFET) evidencing (mainly numerically) different scalings with the linear size of the underlying network according to the initial position of the walkers. If one of the two players is not allowed to move, then the first-encounter problem can be recast into a first-passage problem (MFPT) for which we also obtain exact results for different initial configurations.

The effect of space inhomogeneities on a diffusing particle is studied in the framework of the 1D random walk. The typical time needed by a particle to cross a one-dimensional finite lane, the so-called residence time, is computed possibly in presence of a drift. A local inhomogeneity is introduced as a single defect site with jumping probabilities differing from those at all the other regular sites of the system. We find complex behaviors in the sense that the residence time is not monotonic as a function of some parameters of the model, such as the position of the defect site.

We propose a multi-agent algorithm able to automatically discover relevant regularities in a given dataset, determining at the same time the set of con?gurations of the adopted parametric dissimilarity measure that yield compact and separated clusters. Each agent operates independently by performing a Markovian random walk on a weighted graph representation of the input dataset. Such a weighted graph representation is induced by a speci?c parameter con?guration of the dissimilarity measure adopted by an agent for the search.

The meaning and the features of Generalized Poisson–Kac processes are analyzed in the light of their regularity properties in order to show how the finite propagation velocity, characterizing these models, permits to eliminate the occurrence of singularities in transport models.

This article analyzes the hydrodynamic (continuous) limits of lattice random walks in one spatial dimension. It is shown that a continuous formulation of the process leads naturally to a hyperbolic transport model, characterized by finite propagation velocity, while the classical parabolic limit corresponds to the Kac limit of the hyperbolic model itself. This apparently elementary problem leads to fundamental issues in the theory of stochastic processes and non-equilibrium phenomena, paving the way to new approaches in the field.

Considering the dynamics of non-interacting particles randomly moving on a lattice, the occurrence of a discontinuous transition in the values of the lattice parameters (lattice spacing and hopping times) determines the uprisal of two lattice phases. In this letter we show that the hyperbolic hydrodynamic model obtained by enforcing the boundedness of lattice velocities derived in Giona M., Phys.

The concept of stochastic regularity in lattice models corresponds to the physical constraint that the lattice parameters defining particle stochastic motion (specifically, the lattice spacing and the hopping time) attain finite values. This assumption, that is physically well posed, as it corresponds to the existence of bounded mean free path and root mean square velocity, modifies the formulation of the classical hydrodynamic limit for lattice models of particle dynamics, transforming the resulting balance equations for the probability density function from parabolic to hyperbolic.