Expected space consumption of skip lists

What is the expected space used by the skip list after inserting $n$ elements?

I expect that in the worst case the space consumption may grow indefinitely.

Wikipedia says space $O(n)$.

How can this be proven one way or another?

In this paper it is proven that there exists a constant $\alpha$ such that the probability of the space exceeding $\alpha n$, is less than $1/2^{\Omega(\sqrt{n})}$. Thefore, the more elements there are, the less likely it is to exceed this space bound.

StackExchange Computer Science Q#1713, answer score: 8