8 papers
On the Skorohod topology for functions with values in a completely regular space
Svante Janson
We correct a gap in the proof of a basic theorem by Jakubowski (1986) on the Skorohod topology on the space of functions on [0,1] with values in a completely regular topological sp…
Cyclic and alternating -statistics
Svante Janson
We define cyclic -statistics as a variant of -statistics based on variables that are assumed to be cyclically ordered. We also define alternating -statisti…
A note on Pólya urns: the winner may lead all the time
Svante Janson
Consider a Pólya urn where a drawn ball of colour is replaced together with a fixed number of balls of the same colour. We give a simple proof that if, for example, there…
Moments of balanced Pólya urns
Svante Janson
We give bounds for (central) moments for balanced Pólya urns under very general conditions. In some cases, these bounds imply that moment convergence holds in earlier known results…
Rounding of discrete variables
Svante Janson
Let be a random variable that takes its values in , for some integer , and consider rounded to an integer, either downwards or upwards or to t…
Fringe trees of Patricia tries, compressed binary search trees, and three other random full binary trees
Svante Janson
We study the distribution of fringe trees in Patricia tries (extending earlier results by Ischebeck (2025)) and compressed binary search trees; both cases are random binary trees t…
Almost sure and moment convergence for triangular Pólya urns
Svante Janson
We consider triangular Pólya urns and show under very weak conditions a general strong limit theorem of the form a.s., where is the number…
On semi-restricted Rock, Paper, Scissors
Svante Janson
Spiro, Surya and Zeng (Electron. J. Combin. 2023; arXiv:2207.11272) recently studied a semi-restricted variant of the well-known game Rock, Paper, Scissors; in this variant the gam…