Convergence in the p-Contest
We study asymptotic properties of the following Markov system of N≥3 points in [0, 1]. At each time step, the point farthest from the current centre of mass, multiplied by a constant p>0, is removed and replaced by an independent ζ-distributed point; the problem, inspired by variants of the Bak–Sneppen model of evolution and called a p-contest, was posed in Grinfeld et al. (J Stat Phys 146, 378–40