Journal of Applied Probability: Volume 52 - Issue 1

Asymptotic Properties of Protected Nodes in Random Recursive Trees
Part of:
- Limit theorems
- Combinatorial probability
Hosam M. Mahmoud, Mark D. Ward
Published online by Cambridge University Press:

30 January 2018, pp. 290-297
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We investigate protected nodes in random recursive trees. The exact mean of the number of such nodes is obtained by recurrence, and a linear asymptotic equivalent follows. A nonlinear recurrence for the variance shows that the variance grows linearly, too. It follows that the number of protected nodes in a random recursive tree, upon proper scaling, converges in probability to a constant.

An Optimal Threshold Strategy in the Two-Envelope Problem with Partial Information
Part of:
- Stochastic processes
- Mathematical economics
Martin Egozcue, Luis Fuentes García
Published online by Cambridge University Press:

30 January 2018, pp. 298-304
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In this paper we propose a strategy that gives an optimal lower bound of the average gain for the two-envelope problem within the McDonnell and Abbott (2009) and McDonnell et al. (2011) framework. We obtain this result with partial information about the probability distribution of the envelope's contents.

Journal of Applied Probability