Speaker: Pablo Ferrari - University of Buenos Aires
Abstract
A Poisson line process is the image of a Poisson point process in the plane under the map (a,b)→(at+b)t ∈R. By associating a step with each line of the process, a random surface is obtained. Cutting the surface with vertical planes gives a one-dimensional continuous-time Markov process. The diffusive rescaling of the surface converges to a Gaussian process called the Lévy-Chentsov field.
The hard rod process is a classical traffic model where the plane is interpreted as time-space. Each quasi-particle has a length and travels ballistically until it collides with another quasi-particle, at which point they interchange positions. By identifying lines with the ballistic displacements of the quasi-particles and associating steps with jumps, one can show the law of large numbers, as well as the convergence of the fluctuations in the displacements of the quasi-particles to the Lévy-Chentsov field.