We are interested in the asymptotic analysis of the binary search tree (BST) under the random permutation model. Via an embedding in a continuous time model, we get new results, in particular the asymptotic behavior of the profile.
"Martingales and Profile of Binary Search Trees." Electron. J. Probab. 10 420 - 435, 2005. https://doi.org/10.1214/EJP.v10-257