Recursive splitting of an interval when the proportions are identical and independent random variables

AbstractImagine a stick broken at a random point according to the known distribution function F, the right hand piece being discarded. The remaining left hand piece is then broken according to the same (but rescaled) distribution F ad infinitum. What is the largest piece discarded and at what stage of the process does it occur? Using a basic recursive property, these and related questions are studied, in particular when the distribution F is uniform