We have applied the Ewald-Kornfeld formulation to a tetragonal lattice of point dipoles, in an attempt to examine the effects of geometric anisotropy on the local field distribution. The various problems encountered in the computation of the conditionally convergent summation of the near field are addressed and the methods of overcoming them are discussed. The results show that the geometric an...

One must know the sampling distribution of the estimator (the statistic used to estimate  I shall use   to stand for the statistic used to estimate  ) to make full use of the estimator. The sampling distribution of a statistic is the distribution that would be obtained if you repeatedly drew samples of a specified size from a specified population and computed   on each sample. In other wo...

For random walks {Sn} whose distribution can be embedded in an exponential family large deviation approximations are obtained for the probability that maxo 6 (i) conditionally given S^. and (ii) unconditionally. The method used in the conditional case seems applicable to maxima of a reasonably large class of random fields. For the unconditional probability a more special argu...

Let B be a standard one-dimensional Brownian motion started at 0. Let Lt;v (jBj) be the occupation density of jBj at level v up to time t. The distribution of the process of local times (Lt;v(jBj);v 0) conditionally given Bt = 0 and Lt;0(jBj) = ` is shown to be that of the unique strong solution X of the It^ o SDE

We propose a kernel method to identify finite mixtures of nonparametric product distributions. It is based on a Hilbert space embedding of the joint distribution. The rank of the constructed tensor is equal to the number of mixture components. We present an algorithm to recover the components by partitioning the data points into clusters such that the variables are jointly conditionally indepen...

We show that a large number of elliptic curve L-functions do not vanish at the central point, conditionally on the generalized Riemann hypothesis and on a hypothesis on the regular distribution of the root number. Some hypothesis on the root number is necessary because it has not yet been ruled out that the root number is −1 for almost all elliptic curves. This is the first result of its type f...