Exact extreme, order, and sum statistics in a class of strongly correlated systems.

Even though strongly correlated systems are abundant, only a few exceptional cases admit analytical solutions. In this paper we present a large class of solvable systems with strong correlations. We consider a set of N independent and identically distributed random variables {X_{1},X_{2},.

Extreme Statistics and Spacing Distribution in a Brownian Gas Correlated by Resetting.

We study a one-dimensional gas of N Brownian particles that diffuse independently, but are simultaneously reset to the origin at a constant rate r. The system approaches a nonequilibrium stationary state with long-range interactions induced by the simultaneous resetting. Despite the presence of strong correlations, we show that several observables can be computed exactly, which include the global average density, the distribution of the position of the kth rightmost particle, and the spacing distribution between two successive particles.

Modeling the role of police corruption in the reduction of organized crime: Mexico as a case study.

Among all types of corruption, police corruption is probably the one that most directly hurts society, as those trusted with protecting the people either side with the criminals that victimize the citizens, or are themselves, criminals. However, both corruption and its effects are very difficult to measure quantitatively other than by perception surveys, but the perception that citizens have of this phenomenon may be different from reality. Using a simple agent-based model, we analyze the effect on crime rates as a result of both corruption and the perception of corruption within law-enforcement corporations.

First-passage probabilities and mean number of sites visited by a persistent random walker in one- and two-dimensional lattices.

We study the first passage probability and mean number of sites visited by a discrete persistent random walker on a lattice in one and two dimensions. This is performed by using the multistate formulation of the process. We obtain explicit expressions for the generating functions of these quantities.

Delay in the dispersal of flocks moving in unbounded space using long-range interactions.

Since the pioneering work by Vicsek and his collaborators on the motion of self-propelled particles, most of the subsequent studies have focused on the onset of ordered states through a phase transition driven by particle density and noise. Usually, the particles in these systems are placed within periodic boundary conditions and interact via short-range velocity alignment forces. However, when the periodic boundaries are eliminated, letting the particles move in open space, the system is not able to organize into a coherently moving group since even small amounts of noise cause the flock to break apart.