Using probabilistic tools, this work states a pointwise convergence offunction solutions of the 2-dimensional Boltzmann equation to the functionsolution of the Landau equation for Maxwellian molecules when the collisions become grazing. To this aim, we use the results ofFournier (2000) on the Malliavin calculus for the Boltzmannequation. Moreover, using the particle system introduced by Guérin andMéléard (2003), some simulations of the solution of the Landau equation will be given. This result isoriginal and has not been obtained for the moment by analytical methods.
