Abstract
In this article we consider two well known combinatorial optimization problems (travel-ling salesman and minimum spanning tree), when n points are randomly distributed in a unit p-adic ball of dimension d. We investigate an asymptotic behavior of their solutions at large number of n. It was earlier found that the average lengths of the optimal solutions in both problems are of order n1−1/d. Here we show that standard deviations of the optimal lengths are of order n1/2−1/d if d > 1, and prove that large number laws are valid only for special subsequences of n.
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