Loose Hamilton Cycles in Random 3-Uniform Hypergraphs

In the random hypergraph H = H(n,p;3) each possible triple appears independently with probability p. A loose Hamilton cycle can be described as a sequence of edges {x(i),y(i),(xi+1)} for i = 1,2,...,n/2 where x(1),x(2),...,x(n/2),y(1),y(2),...,y(n/2) are all distinct. We prove that there exists an absolute constant K > 0 such that if p >= Klogn/n(2) then lim(n ->infinity 4/n) Pr(H(n,p;3) contains a loose Hamilton cycle) = 1.