Tunnelling for Large N

In this brief note, by applying the stochastic approach to multiple fields, we estimate the probability of tunneling between vacua in a landscape with $\cal N$ fields. We find that the probability can be enhanced by large $\cal N$. When $\cal N$ saturates the dS entropy of some vacuum, the corresponding vacuum will be extremely unstable and be expected to rapidly decay. We discuss the implications of this result.