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Abstract: We introduce a novel stochastic growth process, the record-driven growthprocess, which originates from the analysis of a class of growing networks in auniversal limiting regime. Nodes are added one by one to a network, each nodepossessing a quality. The new incoming node connects to the preexisting nodewith best quality, that is, with record value for the quality. The emergentstructure is that of a growing network, where groups are formed around recordnodes nodes endowed with the best intrinsic qualities. Special emphasis isput on the statistics of leaders nodes whose degrees are the largest. Theasymptotic probability for a node to be a leader is equal to the Golomb-Dickmanconstant omega=0.624329

. which arises in problems of combinatorical nature.This outcome solves the problem of the determination of the record breakingrate for the sequence of correlated inter-record intervals. The processexhibits temporal self-similarity in the late-time regime. Connections with thestatistics of the cycles of random permutations, the statistical properties ofrandomly broken intervals, and the Kesten variable are given.

Author: C. Godreche, J.M. Luck

Source: https://arxiv.org/

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