Pathintegral approach to turbulence at the example of the Burger's equation

Anomalous scaling in the random-force-driven Burgers equation: A Monte Carlo study.
David Mesterhazy and Karl Jansen, New J.Phys. 13 (2011) 103028
A followup paper where we show that we can sample rare events

A Hybrid Monte Carlo algorithm for sampling rare events in space-time histories of stochastic fields.
G. Margazoglou, L. Biferale, R. Grauer, K. Jansen, D. Mesterhazy, T. Rosenow, R. Tripiccione, Phys. Rev. E 99, 053303 (2019)

Here is a little film, how a shock developes on the lattice

Another film, how structures are created in Burgers turbulence