Ramin Kazemi - Department of Statistics, Imam Khomeini International University, Qazvin, Iran. Saeid Delavar - Department of Statistics, Imam Khomeini International University, Qazvin, Iran.
The purpose of this paper is to provide a precise analysis of the \(t\)-th moment of the profile in random binary digital trees. We assume that the \(n\) input strings are independent and follow a (binary) Bernoulli model. In tries, the main difference with the previous analysis is that we have to deal with an inhomogeneous part in the proper functional equation satisfied by the \(t\)-th moment and in digital search trees with an inhomogeneous part in a proper functional-differential equation. We show that \(t\)-th moment of the profile (\(t\geq 2\)) is asymptotically of the same order as the expected value (\(t=1\)). These results are derived by methods of analytic combinatorics.