  We determined the probability distribution of the combined output power from
twenty five coupled fiber lasers and show that it agrees well with the
Tracy-Widom, Majumdar-Vergassola and Vivo-Majumdar-Bohigas distributions of the
largest eigenvalue of Wishart random matrices with no fitting parameters. This
was achieved with $500,000$ measurements of the combined output power from the
fiber lasers, that continuously changes with variations of the fiber lasers
lengths. We show experimentally that for small deviations of the combined
output power over its mean value the Tracy-Widom distribution is correct, while
for large deviations the Majumdar-Vergassola and Vivo-Majumdar-Bohigas
distributions are correct.
