Common Hyperplane Medians for Random Vectors

Common Hyperplane Medians for Random Vectors

xpm -x and necessarily splits in K[X] into distinct first degree factors so that Da is diagonalizable. Applying this to Dg, for Ek = {x: [g, x] = kx}, we have Eo K and D = YEk, where the sum is direct and taken over all k E K with Ek # 0. Now, if x E D *, gx xg kx for some k E K is equivalent to requiring that x belong to N *. Moreover, y E Ek is equivalent to y E Kx. Then each Ek is a K-subspa...

Random Hyperplane Search Trees

Abstract. A hyperplane search tree is a binary tree used to store a set S of n d-dimensional data points. In a random hyperplane search tree for S, the root represents a hyperplane defined by d data points drawn uniformly at random from S. The remaining data points are split by the hyperplane, and the definition is used recursively on each subset. We assume that the data are points in general p...

Random Walk and Hyperplane Arrangements

Let C be the set of chambers of a real hyperplane arrangement. We study a random walk on C introduced by Bidigare, Hanlon, and Rockmore. This includes various shuuing schemes used in computer science, biology, and card games. It also includes random walks on zonotopes and zonotopal tilings. We nd the stationary distributions of these Markov chains, give good bounds on the rate of convergence to...

Autoregressive Gaussian Random Vectors of First Order

Estimation of Spectral Measure of Stable Random Vectors

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