The martingale decomposition and approximation theorems for a generalized random permanent function

• Autorzy: Rempała G.
• Języki publikacji: EN

Abstrakty

EN

The paper presents some recent developments in the theory ofpermanents for random matrices of independent columns. In particular, it is shown that the theory in a natural way incorporates and extends that of U-statistics of iid real random variables. An extension of the famous martingale decomposition (or H-decomposition) for U-statistics to a certain class of matrix functionals, which includes in particular a classical permanent function, is given.

Słowa kluczowe

EN

martingale decomposition; approximation theorems; generalized random

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2001
• Tom: Vol. 34, nr 2
• Strony: 431--446
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Rempała G.

• Department of Mathematics University of Louisville Natural Sciences Bldg. Louisville, KY 40292, USA

Bibliografia

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• 2. Borovskikh, Y. V. and Korolyuk, V. S. (1994). Random permanents and symmetric statistics, Acta Appl. Math. 36(3), 227-288.
• 3. Lee, A. J. (1990). U-statistics. Theory and Practice, volume 110 of Statistics: Textbooks and Monographs. Marcel Dekker Inc., New York.
• 4. Mine, H. (1978). Permanents. Addison-Wesley Publishing Co., Reading, Mass. With a foreword by Marvin Marcus, Encyclopedia of Mathematics and its Applications, Vol.6.
• 5. Rempała, G. and Wesołowski, J. (2000a). Central limit theorems for random permanents with correlation structure. Manuscript, to appear in Journal of Theoretical Probability.
• 6. Rempała, G. and Wesołowski, J. (2000b). Strong laws of large numbers for random permanents. Manuscript.
• 7. Rempała, G. and Wesołowski, J. (1999). Limiting behavior of random permanents, Statist. Probab. Lett. 45(2), 149-158.
• 8. Ryser, H. J. (1963). Combinatorial Mathematics. Published by The Mathematical Association of America. The Carus Mathematical Monographs, No. 14.
• 9. Valiant, L. (1979). The complexity of computing the permanent, Theoret. Comput. Sc. 8(1), 189-201.
• 10. van Es, A. J. and Helmers, R. (1988). Elementary symmetric polynomials of increasing order, Probab. Theory Related Fields 80(1), 21-35.