As an attempt to understand the statistical properties of turbulence, Burgers studied solutions to Burgers equation with white noise initial data. More generally one may study a scalar conservation with white noise or Markovian initial condition. After the works of Groeneboom, Chabanol-Duchon, Bertoin, Avallaneda-E, Menon-Srinivasan,...we know that the class of spectrally negative Markov...