Collision probabilities in the rarefaction fan of asymmetric exclusion processes

We consider the one-dimensional asymmetric simple exclusion process (ASEP) in which particles jump to the right at rate p is an element of (1/2, 1.] and to the left at rate 1 - p, interacting by exclusion. In the initial state there is a finite region such that to the left of this region all sites are occupied and to the right of it all sites are empty. Under this initial state, the hydrodynamical limit of the process converges to the rarefaction fan of the associated Burgers equation. In particular suppose that the initial state has first-class particles to the left of the origin, second-class particles at sites 0 and I, and holes to the right of site I. We show that the probability that the two second-class particles eventually collide is (1 + p)/(3p), where a collision occurs when one of the particles attempts to jump over the other. This also corresponds to the probability that two ASEP processes. started from appropriate initial states and coupled using the so-called ""basic coupling,"" eventually reach the same state. We give various other results about the behaviour of second-class particles in the ASEP. In the totally asymmetric case (p = 1) we explain a further representation in terms of a multi-type particle system, and also use the collision result to derive the probability of coexistence of both clusters in a two-type version of the corner growth model.

Multiclass Hammersley-Aldous-Diaconis process and multiclass-customer queues

In the Hammersley-Aldous-Diaconis process, infinitely many particles sit in R and at most one particle is allowed at each position. A particle at x, whose nearest neighbor to the right is at y, jumps at rate y - x to a position uniformly distributed in the interval (x, y). The basic coupling between trajectories with different initial configuration induces a process with different classes of particles. We show that the invariant measures for the two-class process can be obtained as follows. First, a stationary M/M/1 queue is constructed as a function of two homogeneous Poisson processes, the arrivals with rate, and the (attempted) services with rate rho > lambda Then put first class particles at the instants of departures (effective services) and second class particles at the instants of unused services. The procedure is generalized for the n-class case by using n - 1 queues in tandem with n - 1 priority types of customers. A multi-line process is introduced; it consists of a coupling (different from Liggett's basic coupling), having as invariant measure the product of Poisson processes. The definition of the multi-line process involves the dual points of the space-time Poisson process used in the graphical construction of the reversed process. The coupled process is a transformation of the multi-line process and its invariant measure is the transformation described above of the product measure.

Democracy on the Edge: Limits and Possibilities in the Implementation of an Urban Reform Agenda in Brazil

The 1990s in Brazil were a time of institutional advances in the areas of housing and urban rights following the signing of the new constitution in 1988 that incorporated the principles of the social function of cities and property, recognition of the right to ownership of informal urban squatters and the direct participation of citizens in urban policy decision processes. These propositions are the pillars of the urban reform agenda which, since the creation of the Ministry of Cities by the Lula government, has come under the federal executive branch. This article evaluates the limitations and opportunities involved in implementing this agenda on the basis of two policies proposed by the ministry - the National Cities Council and the campaign for Participatory Master Plans - focusing the analysis on government organization in the area of urban development in its relationship with the political system and the characteristics of Brazilian democracy. Resume Au Bresil, les annees 1990 ont ete marquees par des progres institutionnels en matiere de logement et de droits urbains, dans le sillage de la Constitution de 1988 qui integre les principes d`une fonction sociale de la ville et de la propriete urbaine, ainsi que la reconnaissance du droit a la propriete pour les squatters urbains et la participation directe des citoyens aux processus d`elaboration des politiques urbaines. Ce sont egalement les piliers du programme de reforme urbaine qui releve de l`executif federal depuis la creation d`un ministere des Villes par le gouvernement Lula. Pour evaluer les limites et potentiels lies a la mise en place de ce programme, cet article s`appuie sur deux politiques publiques proposees par le ministere, le Conseil national des villes et la campagne en faveur des Plans directeurs participatifs, en analysant plus particulierement l`organisation gouvernementale en matiere d`urbanisme par rapport au systeme politique et aux caracteristiques de la democratie bresilienne.