We study the Wigner minor process, which is a sequence of appropriately scaled $N\times N$ upper left corners of a doubly infinite symmetric array of i.i.d. random variables. It is well known that the top eigenvalue of these matrices almost surely converges to 2 as $N$ goes to infinity, with fluctuations given by the Tracy-Widom distribution. These results can be viewed as the law of large numbers and the central limit theorem. We make a step further and establish the analogue of the Hartman-Winter law of iterated logarithm in this setting. This result was initially coined as a law of fractional logarithm (LFL) by E. Paquette and O. Zeitouni, who resolved the special case of GUE matrices. Our work verifies the 10-year-old conjecture by these authors, proving the LFL in full generality for both symmetry classes. Additionally, we show that the correlation between the top eigenvalues in the minor process becomes weaker as the difference between the sizes of the minors increases. We establish the precise description of the  resulting decorrelation transition, extending the result of J. Forrester and T. Nagao for the GUE case. The talk is based on the recent joint works with Z. Bao, G. Cipolloni, L. Erd{\H o}s and J. Henheik.