Scientific publications

We study products of discrete random variables forming nontransitive sets of dice with equal means and variances, and independent continuous random variables distributed according to the Weibull or Pareto laws. It is shown that the functions describing stochastic precedence converge to those of the original discrete model as the distribution parameter increases. For each distribution family, we establish critical parameter values beyond which nontransitivity is stably restored in all sets. The behavior of the sets is shown to be non-monotonic in certain cases: nontransitivity may emerge temporarily at low parameter values, become lost as the parameter increases, and subsequently reappear (in some sets, multiple times) including cases where the dominance cycle is reversed. Various forms of this effect are explored.