Finding Euclidean Minimum Spanning Tree

Question

Given a set of point $P$. Find the euclidean minimum spanning tree where each points is equally distributed on the plane using randomization.

We can solve this problem with Prim's algorithm in $O(n^2)$ which is too slow. I've found an algorithm called Delanuay Triangulation but is there any other ways to solve this problem in $O(n log n)$ or faster?