Lower Bounds for Probabilities of Embedding with Arbitrary Margin

The notion of compact embedding introduced by J. Golic is generalized. The lower estimations are deduced for the mathematical expectation of the probability of embedding with a given margin a segment of the sequence of independent equally distributed random quantities over the N-element alphabet into the sequence of independent random quantitieshaving the uniform distribution on the same alphabet. These estimations refine the known evaluations for the probability of embedding with a given margin and, in particular, for the probability of compact embedding.