We study the distribution P(\omega) of the random variable \omega = x_1/(x_1 + x_2), where x_1 and x_2 are the wealths of two individuals selected at random from the same tempered Paretian ensemble characterized by the distribution \Psi(x) \sim \phi(x)/x^{1 + \alpha}, where \alpha 0 is the...

We focus on two models of nearest-neighbour random walks on d-dimensional regular hyper-cubic lattices that are usually assumed to be identical—the discrete-time Polya walk, in which the walker steps at each integer moment of time, and the Montroll–Weiss continuous-time random walk in which...

We consider a lattice model of the annihilation process A+B→B, when a mobile prey A is chased by identical, independent predators B performing random motions until one of them finds A and destroys it. It is assumed that each predator follows some “most probable” trajectory around which it...

We study the distribution P(ω) of the random variable ω=x1/(x1+x2), where x1 and x2 are the wealths of two individuals selected at random from the same tempered Paretian ensemble characterized by the distribution Ψ(x)∼ϕ(x)/x1+α, where α0 is the Pareto index and ϕ(x) is the cut-off...

We study the kinetics of diffusion-controlled A+B→B reactions, in which both species are moving randomly on a d-dimensional lattice and react upon encounters, provided that both species are in reactive states. Particles’ reactivity fluctuates randomly between active and passive forms. We...

We consider a simple model of annihilation reaction, when particles are located on a regular lattice, one of them presenting a fluctuating activity. Time-correlated fluctuations are addressed. The reaction probability and the reaction function are determined exactly. It is shown that the usual,...

We study the dynamics of a tracer particle, which performs a totally directed random walk in an adsorbed monolayer composed of mobile hard-core particles undergoing continuous exchanges with a vapour phase. In terms of a mean-field-type approach, based on the decoupling of the...