Abstract
Michel Talagrand’s mini-course on Matching Theorems provided a clear, concise, and unified introduction to many of the important matching theorems based on new applications and constructions of majorizing measures. This exposition attempts to record the ideas from those lectures. None of the research presented here is due to the authors. A more general presentation of Talagrand’s ideas appears in Talagrand (1991a).
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References
Ajtai, M., Komlos, G., and Tusnady, G. (1984). On optimal matchings. Combinatorial 4, 259–264.
Dudley, R. M. (1967). The sizes of compact subsets of Hilbert space and continuity of Gaussian processes. J. Funct. Anal. 1, 290–330.
Dudley, R. M. (1973). Sample functions of the Gaussian process. Ann. Probab. 1, 66–103.
Fernique, X. (1975). Régularité des trajectoires des fonctions aléatoires gaussiennes. Ecole d’Eté de Probabilités de St-Flour 1974. Lec. Notes in Math. 480, 1–96. Springer, Berlin Heidelberg.
Giné, E. and Zinn, J. (1984). Some limit theorems for empirical processes. Ann. Probab. 12, 929–989.
Jain, N. C. and Marcus, M. B. (1975) Central limit theorem for C (S)-valued random variables. J. Funct. Anal. 19, 216–231.
Ledoux, M. and Talagrand, M. (1991). Probability in Banach Spaces. Springer-Verlag.
Leighton, T. and Shor, P. W. (1989). Tight bounds for minimax grid matching with applications to the average case analysis of algorithms. Combinatorica 9, 161–187.
Marcus, M. B. (1974). The ε-entropy of some compact subsets of l p. J. Approximation Theory 10, 304–312.
Papadimitriou, C. H. and Steiglitz, K. (1982). Combinatorial Optimization, Algorithms and Complexity. Prentice Hall, NJ.
Preston, C. (1971). Banach spaces arising from some integral inequalities. Indiana Math. J. 20, 997–1015.
Preston, C. (1972). Continuity properties of some Gaussian processes. Ann. Math. Statist. 43, 285–292.
Talagrand, M. (1987). Regularity of Gaussian processes. Acta Math. 159, 99–149.
Talagrand, M. (1991a). Matching theorems and empirical discrepency computations using majorizing measures. Manuscript.
Talagrand, M. (1991b). A simple proof of the majorizing measure theorem. Manuscript.
Talagrand, M. (1992a). The Ajtai-Komlos-Tusnady matching theorem for general measures. In this volume.
Talagrand, M. (1992b). Matching random samples in dimension 3 (or more). Forthcoming.
Talagrand, M. (1992c). Matching random samples in many dimensions. To appear in Ann. Appl. Probab.
Yukich, J. (1992a). The exponential integrability of transportation cost. Preprint.
Yukich, J. (1992b). Some generalizations of the Euclidean two-sample matching problem. In this volume.
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Hahn, M.G., Shao, Y. (1992). An Exposition of Talagrand’s Mini-Course on Matching Theorems. In: Dudley, R.M., Hahn, M.G., Kuelbs, J. (eds) Probability in Banach Spaces, 8: Proceedings of the Eighth International Conference. Progress in Probability, vol 30. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0367-4_1
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