ON RANDOM COVERING OF A CIRCLE

Let Xj ; j = 1; 2; :::; n be the independent and identically distributed random vectors which take the values on the unit circumference.Let Sn be the area of the convex polygon having Xj as vertices. The paper by Nagaev and Gold¯eld (1989) has proved the asymptotic normality of random variableSn. Our main aim is to show that the random variableSn can be represented as a sum of functions of uniform spacings. This allows us to apply known results related to uniform spacings for the analysis of Sn.