On a Tail Bound for Root-Finding in Randomly Growing Trees

Sam Justice, N. D. Shyamalkumar

We re-examine a lower-tail upper bound for the random variable $$X=\prod _{i=1}^{\infty }\min \left\{\sum _{k=1}^i{E}_k,1\right\},$$ where $E_1,E_2,\dots \stackrel{iid}{\sim }\text{Exp}(1)$…