On random determinants
Author:
A. Dembo
Journal:
Quart. Appl. Math. 47 (1989), 185-195
MSC:
Primary 62H10; Secondary 60E05, 60F05, 68T05
DOI:
https://doi.org/10.1090/qam/998095
MathSciNet review:
998095
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Abstract: The distribution of the determinant $\left ( {{U^T}U} \right )$, where $U$ is a $P \times N$ matrix $\left ( {P \le N} \right )$ composed of $P \times N$ i. i. d. random variables with symmetrical distribution is investigated. In particular, explicit formulas for the first two moments are obtained, as well as the higher moments for standard normal distribution of the elements of $U$. These formulas extend the previously known results for $P = N$.
- Amir Dembo, On the capacity of associative memories with linear threshold functions, IEEE Trans. Inform. Theory 35 (1989), no. 4, 709–720. MR 1013681, DOI https://doi.org/10.1109/18.32149
- R. Fortet, Random determinants, J. Research Nat. Bur. Standards 47 (1951), 465–470. MR 0047274
- P. Turán, On a problem in the theory of determinants, Acta Math. Sinica 5 (1955), 411–423 (Chinese, with English summary). MR 73555
- H. Nyquist, S. O. Rice, and J. Riordan, The distribution of random determinants, Quart. Appl. Math. 12 (1954), 97–104. MR 63591, DOI https://doi.org/10.1090/S0033-569X-1954-63591-8
- A. Prékopa, On random determinants. I, Studia Sci. Math. Hungar. 2 (1967), 125–132. MR 211439
- Samuel S. Wilks, Mathematical statistics, A Wiley Publication in Mathematical Statistics, John Wiley & Sons, Inc., New York-London, 1962. MR 0144404
G. E. Forsythe and J. W. Tukey, The extent of n random unit vectors (abstract), Bull. Amer. Math. Soc. 58, 502 (1952)
- John Riordan, An introduction to combinatorial analysis, Wiley Publications in Mathematical Statistics, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1958. MR 0096594
- A. N. Shiryayev, Probability, Graduate Texts in Mathematics, vol. 95, Springer-Verlag, New York, 1984. Translated from the Russian by R. P. Boas. MR 737192
Kömlos, Estimate for singular matrices, unpublished manuscript, also on pp. 347–350 of Random Graphs by B. Bollobas, Academic press, 1985
Particle Systems, Random Matrices and Large Deviations, AMS Series on Contemporary Math., vol. 41, 1984
A. Dembo, On random determinants, LCDS/CCS Report #87-3, Division of Applied Mathematics, Brown University
A. Dembo, On the Capacity of Associative Memories with Linear Threshold Functions, to appear in IEEE Trans. on Information Theory
R. Fortet, Random determinants, J. Research. Nat. Bur. Standards 17, 465–470 (1951)
P. Turan, On a problem in the theory of determinants, Acta. Math. Sinica 5, 417–423 (1955)
H. Nyquist, S. O. Rice, and J. Riordan, The distribution of random determinants, Quart. Appl. Math. 12, 97–102 (1954)
A. Prekopa, On random determinants I, Studia Scientiarum Mathematicarum Hungarica 2, 125–132 (1967)
S. S. Wilks, Mathematical Statistics, Wiley, New York, London, 1962
G. E. Forsythe and J. W. Tukey, The extent of n random unit vectors (abstract), Bull. Amer. Math. Soc. 58, 502 (1952)
J. Riordan, An introduction to combinatorial analysis, Wiley, New York, London, 1958
A. N. Shiryayev, Probability, Springer-Verlag, New York, 1984
Kömlos, Estimate for singular matrices, unpublished manuscript, also on pp. 347–350 of Random Graphs by B. Bollobas, Academic press, 1985
Particle Systems, Random Matrices and Large Deviations, AMS Series on Contemporary Math., vol. 41, 1984
A. Dembo, On random determinants, LCDS/CCS Report #87-3, Division of Applied Mathematics, Brown University
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Article copyright:
© Copyright 1989
American Mathematical Society
