  Simulated tempering is a popular method of allowing MCMC algorithms to move
between modes of a multimodal target density {\pi}. The paper [24] introduced
the Annealed Leap-Point Sampler (ALPS) to allow for rapid movement between
modes. In this paper, we prove that, under appropriate assumptions, a suitably
scaled version of the ALPS algorithm converges weakly to skew Brownian motion.
Our results show that under appropriate assumptions, the ALPS algorithm mixes
in time O(d[log(d)]^2 ) or O(d), depending on which version is used.
