Shock fluctuations in a particle system

The hydrodynamical behavior of the one-dimensional nearest neighbor asymmetric simple exclusion process is described by the inviscid Burgers equation. This equation has shock wave solutions and when the density before the shock is 0, the shock, at the particle level, has stable shape and rigidly fluctuates around its average position with Brownian law, [20] and [8]. We prove here that in the hydrodynamical limit such fluctuations are determined exclusively by the initial particle configuration and are not influenced by the randomness produced by the evolution Le comportement hydrodynamique du processus de simple exclusion entre plus proches voisins asymmetriques en dimension un est decrit par l'equation de Burgers inviscide. Cette equation a des solutions ondes de choc, et quand la densite est nulle en avant du choc, le choc au niveau particulaire a une forme stable et fluctue