Strong law of large numbers for the middle part of a sample

Let {X_n}_n=1 be a sequence of independent, symmetric random variables and let {X_in}_i=1ⁿ be the absolute order statistics. The rate of growth of and X_2,n is investigated for n.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 166, pp. 25–31, 1988.