The sequence of partial maxima for i.i.d. random variables is considered. Two theorems concerning the sample behaviour of the maxima are proved. Also a large deviations result is given, connected with weak convergence to the double exponential distribution.
"The Rate of Growth of Sample Maxima." Ann. Math. Statist. 43 (4) 1185 - 1196, August, 1972. https://doi.org/10.1214/aoms/1177692470