Stochastic dynamics of discrete curves: exclusion processes and hydrodynamic limits
G. Fayolle (INRIA, Research Center Paris-Rocquencourt, France)
In statistical physics, interplay between discrete and continuous description is a recurrent question, which in some cases can be answered quite rigorously via probabilistic methods. As for reaction-diffusion systems, this amounts to studying fluid or hydrodynamic limits. Here we considerer the problem of random curves subjected to stochastic deformations (or reactions with regard to polymers or biology), and we show that it can be rephrased in terms of interacting particle exclusion processes. To derive hydrodynamic equations, a new functional approach is proposed and illustrated by some classical models (ASEP, ABC, etc).