The Diffusion Monte Carlo method is devoted to the computation of
electronic ground-state energies of molecules. In this paper, we focus on
implementations of this method which consist in exploring the
configuration space with a fixed number of random walkers evolving
according to a stochastic differential equation discretized in time. We
allow stochastic reconfigurations of the walkers to reduce the
discrepancy between the weights that they carry. On a simple
one-dimensional example, we prove the convergence of the method for a
fixed number of reconfigurations when the number of walkers tends to
+∞ while the timestep tends to 0. We confirm our theoretical
rates of convergence by numerical experiments. Various resampling
algorithms are investigated, both theoretically and numerically.