期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2016
卷号：XIII
期号：2
页码：1095-1122
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：In the classical leader election procedure all players toss coins independentlyand those who get tails leave the game, while those who get heads move tothe next round where the procedure is repeated. We investigate a generalizion ofthis procedure in which the labels (positions) of the players who remain in the gameare determined using an integer-valued random walk. We study the asymptotics ofsome relevant quantities for this model such as: the positions of the persons whoremained after n rounds; the total number of rounds until all the persons among1, 2, . . . ,M leave the game; and the number of players among 1, 2, . . . ,M who survivedthe first n rounds. Our results lead to some interesting connection withGalton-Watson branching processes and with the solutions of certain stochasticfixedpoint equations arising in the context of the stability of point processes underthinning. We describe the set of solutions to these equations and thus provide acharacterization of one-dimensional point processes that are stable with respect tothinning by integer-valued random walks.
关键词：Galton-Watson branching process; leader-election procedure; random;sieve; restricted self-similarity; stable point process; stochastic-fixed point equation.
