Cutoff for Random Walk on Dynamical Erdos-Renyi

We study the behaviour of random walk on dynamical percolation. In this model, the edges of a graph are either open or closed and refresh their status at rate μ, while at the same time a random walker moves on G at rate 1, but only along edges which are open. In this talk I shall present recent results proving cutoff in the case when G is the complete graph and the bond percolation parameter is of order 1/n, ie we consider a random walk on dynamical Erdos-Renyi graph. We do this via an explicit coupling argument. Joint work with Perla Sousi