A recent paper of Melbourne & Stuart, A note on diffusion limits of chaotic skew product flows, Nonlinearity 24 (2011) 1361–1367, gives a rigorous proof of convergence of a fast-slow deterministic system to a stochastic differential equation with additive noise. In contrast to other approaches, the assumptions on the fast flow are very mild. In this paper, we extend this result from continuous ...

Cayley maps are combinatorial structures built upon graphs on a group. As such the original group embeds in their of automorphisms, and one can ask which situation two coincide (one then calls map  a mapical regular representation or MRR) with what probability. The first question was answered by Jajcay. In this paper we tackle probabilistic version, prove that as groups get larger proporti...