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On the weighted Euclidean matching problem in d

Birgit Anthes, Ludger Rüschendorf (2001)

Applicationes Mathematicae

A partitioning algorithm for the Euclidean matching problem in d is introduced and analyzed in a probabilistic model. The algorithm uses elements from the fixed dissection algorithm of Karp and Steele (1985) and the Zig-Zag algorithm of Halton and Terada (1982) for the traveling salesman problem. The algorithm runs in expected time n ( l o g n ) p - 1 and approximates the optimal matching in the probabilistic sense.

On weighted U-statistics for stationary random fields

Jana Klicnarová (2017)

Kybernetika

The aim of this paper is to introduce a central limit theorem and an invariance principle for weighted U-statistics based on stationary random fields. Hsing and Wu (2004) in their paper introduced some asymptotic results for weighted U-statistics based on stationary processes. We show that it is possible also to extend their results for weighted U -statistics based on stationary random fields.

One-dimensional finite range random walk in random medium and invariant measure equation

Julien Brémont (2009)

Annales de l'I.H.P. Probabilités et statistiques

We consider a model of random walks on ℤ with finite range in a stationary and ergodic random environment. We first provide a fine analysis of the geometrical properties of the central left and right Lyapunov eigenvectors of the random matrix naturally associated with the random walk, highlighting the mechanism of the model. This allows us to formulate a criterion for the existence of the absolutely continuous invariant measure for the environments seen from the particle. We then deduce a characterization...

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