We consider the maximum of the periodogram based on an infinite variance heavy-tailed sequence. For $\alpha < 1$ we show that the maxima constitute a weakly convergent sequence and find its limiting distribution. For $1 \leq \alpha < 2$ we show that the sequence of the maxima is not tight and find a normalization that makes it tight.
"The maximum of the periodogram for a heavy-tailed sequence." Ann. Probab. 28 (2) 885 - 908, April 2000. https://doi.org/10.1214/aop/1019160264