(Received November 5, 1992; revised March 18, 1993)
Abstract. Let X = (Xij)n×n be a random matrix whose elements are independent Bernoulli random variables, taking the values 0 and 1 with probability qij and pij (pij + qij = 1) respectively. Upper and lower bounds for the probabilities of m non-overlapping occurrences of a square submatrix with all its elements being equal to 1, are obtained. Some Poisson convergence theorems are established for n \to \infty. Numerical results indicate that the proposed bounds perform very well, even for moderate and small values of n.
Key words and phrases: Random matrix, Bernoulli random variables, Poisson approximation, patterns, consecutive-k-out-of-n:F system.
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