First-Passage Statistics of Extreme Values

Theoretical concepts from nonequilibrium statistical physics such as scaling and correlations are used to analyze first-passage processes involving extreme values. The focus of this talk is statistics of the running maxima, defined as the largest variable in a sequence of random variables. In particular, the running maxima of multiple independent sequences of stochastic variables are compared. The probability that these maxima remain perfectly ordered decays algebraically with the number of random variables, and the decay exponent characterizing this decay is nontrivial. Exact solutions for the scaling exponents will be discussed for uncorrelated variables as well as Brownian trajectories which are correlated. Relevance of such statistical measures for analysis of empirical data will be discussed as well.