  We consider two mean-field models of structural glasses, the random energy
model (REM) and the $p$-spin model (PSM), and we show that the finite-size
fluctuations of the freezing temperature are described by extreme-value
statistics (EVS) distributions, establishing an unprecedented connection
between EVS and the freezing transition of structural glasses. For the REM, the
freezing-temperature fluctuations are described by the Gumbel EVS distribution,
while for the PSM the freezing temperature fluctuates according to the
Tracy-Widom (TW) EVS distribution, which has been recently discovered within
the theory of random matrices. For the PSM, we provide an analytical argument
showing that the emergence of the TW distribution can be understood in terms of
the statistics of glassy metastable states.
