Summary: Under general assumptions on the initial data, we show that the entropy solution \((x, t)\mapsto u(x, t)\) of the one-dimensional inviscid Burgers’ equation is the velocity function of a sticky particles model whose initial mass distribution is the Lebesgue measure. Precisely, the particles trajectories \((x, t)\mapsto X_{0, t}(x)\) are given by a forward flow: \(\forall \,(x,s,t)\in \mathbb{R}\times \mathbb{R}_+\times \mathbb{R}_+\), \(X_{0,s+t}(x)=X_{s,t}\big(X_{0,s}(x)\big)\) and \(\frac{\partial }{\partial t} X_{s,t} = u(X_{s,t},s+t)= E[u(\cdot ,s)|X_{s,t}];\,\, u(x,t)=\mathrm{E}[u(\cdot ,0)|X_{0,t}=x]\).{
©2012 American Institute of Physics}