| Autor: |
Saha, Nikita, Chakraborty, Soubhik |
| Předmět: |
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| Zdroj: |
AIP Conference Proceedings; 6/16/2022, Vol. 2471 Issue 1, p1-6, 6p |
| Abstrakt: |
This paper gives a probabilistic analysis of a determinant of order 2 and 3 in.which the elements are i.i.d. U(1, 2, ..., k) variates. The distribution of D is a non-uniform one inspite of its elements being uniformly distributed. The general distribution of D is complex even for order 2 of D. However, the distribution of D for k =2 and k=3 are obtained hen D is of order 2. Further, if D is of order 2, P (− r [ (k + 1) (2 k+1)] 2 18 − (k + 1) 4 8 < D < r [ (k + 1) (2 k + 1) ] 2 18 − (k + 1) 4 8 ) ≥ 1 − 1 r 2 and. if D is of order 3 P ( − r 6 [ (k+1)(2k + 1) 6 ] 3 − 18 ( k + 1 2) 4 [ (k + 1) (2 k + 1) 6 ] + 12 ( k + 1 2) 6 ≤ D ≤ r 6 [ (k + 1) (2 k + 1) 6 ] 3 − 18 ( k + 1 2) 4 [ (k + 1) (2 k + 1) 6 ] + 12 ( k + 1 2) 6 ) ≥ 1 − 1 r 2 using Chebyshev's inequality. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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