The tail distribution of the Derivative martingale and the global minimum of the branching random walk
Abstract
In a seminal paper Biggins and Kyprianou BKy04 proved the existence of a non degenerate limit for the Derivative martingale of the branching random walk. As shown in Aid11 and Mad11, this is an object of central importance in the study of the extremes of the branching random walk. In this paper we investigate the tail distribution of the limit of the Derivative Martingale by mean of the study of the global minimum of the branching random walk. This new approach leads us to extend the results of Gui90 and Bur09 under slighter assumptions.
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