Hi everyone!

I've got $\displaystyle n$ uniformly distributed iid random variables $\displaystyle X_i\backsim U(0,1)$.

Then I sort them ($\displaystyle i>j \rightarrow X_i > X_j$).

My interest lies in

$\displaystyle Y = X_{i+1}-X_{i}$

the distance between two adjacent values.

What I'd like to know is the distribution of $\displaystyle Y$. I'm working on a delta-encoding method (storing a sorted list by their differences indead of directly storing the values) and this would help me understand what values I can expect. So a decent approximation is good enough for me.

Thanks a lot!