  We consider in this paper random batch particle methods for efficiently
solving the homogeneous Landau equation in plasma physics. The methods are
stochastic variations of the particle methods proposed by Carrillo et al. [J.
Comput. Phys.: X 7: 100066, 2020] using the random batch strategy. The
collisions only take place inside the small but randomly selected batches so
that the computational cost is reduced to $O(N)$ per time step. Meanwhile, our
methods can preserve the conservation of mass, momentum, energy and the decay
of entropy. Several numerical examples are performed to validate our methods.
