EVS for uncorrelated random variables: the three limiting distributions (Gumbel, Frechet and Weibull). Simple examples of EVS for correlated random variables: (i) Weakly Correlated: Ornstein-Uhlenbeck process (particle moving in a harmonic potential), limiting distribution of the maximum is the same as that of uncorrelated variables; (ii) Strongly Correlated: Brownian motion - the limiting distribution is half-Gaussian: different from that of the uncorrelated case.
Variety of constrained Brownian motions. Random Matrices.
Path-integral (Feynman-Kac) computation of the maximum distribution. Application to: (i) Brownian Bridge; (ii) Brownian Excursion; (iii) Brownian Meander; (iv) Fluctuating (1+1)-dimensional Interfaces: Airy distribution function (applications in computer science).
Large deviations of the maximum eigenvalue: probability of rare fluctuations. Wishart radom matrices: average density of states (Marcenko-Pastur law), maximum eigenvalue (Tracy-Widom again), minimum eigenvalue (when different from Tracy-Widom), application to Quantum Entanglement problem.
Longest increasing subsequence problem. Hamersley process - interacting particle systems. Directed polymer. (2+1)-dimensional directed percolation. Sequence matching problem. Maximum Agreement SubTree problem in Phylogeny. Etc.