Solution to the OK Corral model via decoupling of Friedman's urn (Q1868456)

The paper investigates the OK Corral model using other mathematical tools than the classical ones, which the results of \textit{D. Williams} and \textit{P. McIlroy} [Bull. Lond. Math. Soc. 30, No. 2, 166-170 (1998; Zbl 0933.60006)] and the first author [ibid. 31, No. 5, 601-606 (1999; Zbl 0933.60007)] are based on. Instead of computing the probabilities for the OK Corral process directly, the authors show the connection between this model and the Friedman's urn, solving the relevant problem for the urn firstly. This task is achieved by using H. Rubin's construction to decouple the urn. This construction is based on two independent birth processes of continuous parameter, having the same distribution as the Friedman's urn, which allows to compute the derived distributions. The paper obtains the exact expression for the probability of survivals of exactly \(S\) gunmen, given an initially fair configuration.