This paper proves a Berry–Esseen theorem for sample quantiles of strongly-mixing random variables under a polynomial mixing rate. The rate of normal approximation is shown to be O(n) as n→∞, where n denotes the sample size. This result is in sharp contrast to the case of the sample mean of strongly-mixing random variables where the rate O(n) is not known even under an exponential strong mixing ...

Abstract We study the rates of estimation of finite mixing distributions, that is, the parameters of the mixture. We prove that under some regularity and strong identifiability conditions, around a given mixing distribution with m0 components, the optimal local minimax rate of estimation of a mixing distribution with m components is n−1/(4(m−m0)+2). This corrects a previous paper by Chen (1995)...

We have calculated the evolution of low metallicity red giant stars under the assumption of deep mixing between the convective envelope and the hydrogen burning shell. We find that the extent of the observed abundance anomalies, and in particular the universal O-Na anticorrelation, can be totally explained by mixing which does not lead to significant helium enrichment of the envelope. On the ot...

The dynamics of infectious diseases that are spread through direct contact have been proven to depend on the strength of community structure or modularity within the underlying network. It has been recently shown that weighted networks with similar modularity values may exhibit different mixing styles regarding the number of connections among communities and their respective weights. However, t...

We consider random walks in strong-mixing random Gibbsian environments in Z, d ≥ 2. Based on regeneration arguments, we will first provide an alternative proof of Rassoul-Agha’s conditional law of large numbers (CLLN) for mixing environment [8]. Then, using coupling techniques, we show that there is at most one nonzero limiting velocity in high dimensions (d ≥ 5).

Hare1 and Puri (1990) established the weak convergence of a class of the serial linear rank statistics with bounded score functions and regression constants when the random variables are q-mixing or strong mixing. This paper extends these results to the case when the score functions as well as the regression constants are not necessarily bounded. AMS Subject Classifications: Primary 60B10, 60F05.

Strong-flavor and parity a priori mixing in hadrons are shown to describe well the experimental evidence on weak radiative decays of hyperons. An independent determination of the a priori mixing angles is performed. The values obtained for them are seen to have a universality–like property, when compared to their values in non-leptonic decays of hyperons.

The work is giving estimations of the discrepancy between solutions of the initial and the homogenized problems for a one-dimensional second-order elliptic operators with random coefficients satisfying strong or uniform mixing conditions. We obtain several sharp estimates in terms of the corresponding mixing coefficient.

The connection between general moment conditions and the applicability of strong laws of large numbers for a sequence of identically distributed ρ-mixing random variables are obtained. The results obtained generalize the result of Petrov (1996, Statist. Probab. Lett. 26, 377-380) to ρ-mixing sequences and NA sequences.