  The Kepler-36 system consists of two planets that are spaced unusually close
together, near the 7:6 mean motion resonance. While it is known that mean
motion resonances can easily form by convergent migration, Kepler-36 is an
extreme case due to the close spacing and the relatively high planet masses of
4 and 8 times that of the Earth. In this paper, we investigate whether such a
system can be obtained by interactions with the protoplanetary disc. These
discs are thought to be turbulent and exhibit density fluctuations which might
originate from the magneto-rotational instability. We adopt a realistic
description for stochastic forces due to these density fluctuations and perform
both long term hydrodynamical and N-body simulations. Our results show that
planets in the Kepler-36 mass range can be naturally assembled into a closely
spaced planetary system for a wide range of migration parameters in a turbulent
disc similar to the minimum mass solar nebula. The final orbits of our
formation scenarios tend to be Lagrange stable, even though large parts of the
parameter space are chaotic and unstable.
