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We formulate the problem of finding the probability that the determinant of amatrix undergoes the least change upon perturbation of one of its elements,provided that most or all of the elements of the matrix are chosen at randomand that the randomly chosen elements have a fixed probability of beingnon-zero. Also, we show that the procedure for finding the probability that thedeterminant undergoes the least change depends on whether the random variablesfor the matrix elements are continuous or discrete.

Least change in the Determinant or Permanent of a matrix under perturbation of a single element: continuous and discrete cases