Almost sure convergence of the minimum bipartite matching functional in Euclidean space
| Autor: | Boutet De Monvel, J., Martin, Olivier |
|---|---|
| Přispěvatelé: | Center for Hearing and Communication Research, Karolinska Institutet [Stockholm], Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Le Vaou, Claudine |
| Jazyk: | angličtina |
| Rok vydání: | 2002 |
| Předmět: |
Statistics::Theory
Mathematics::Commutative Algebra Probability (math.PR) [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC] F.2.2 G.3 [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO] Mathematics::Probability Optimization and Control (math.OC) [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] FOS: Mathematics Mathematics - Combinatorics Mathematics::Metric Geometry Combinatorics (math.CO) [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] Mathematics - Optimization and Control Mathematics - Probability |
| Zdroj: | Combinatorica Combinatorica, Springer Verlag, 2002, 22, pp.523-530 |
| ISSN: | 0209-9683 1439-6912 |
| Popis: | Let $L_N = L_{MBM}(X_1,..., X_N; Y_1,..., Y_N)$ be the minimum length of a bipartite matching between two sets of points in $\mathbf{R}^d$, where $X_1,..., X_N,...$ and $Y_1,..., Y_N,...$ are random points independently and uniformly distributed in $[0,1]^d$. We prove that for $d \ge 3$, $L_N/N^{1-1/d}$ converges with probability one to a constant $\beta_{MBM}(d)>0$ as $N\to \infty $. Comment: To appear in Combinatorica |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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