Convergence in law of the minimum of a branching random walk
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In this article, the authors considered the super-critical branching random walk and proved that a convergence in law holds, giving the analog of a well-known result of Bramson [Mem. Amer. Math. Soc. 44 (1983) iv+190] in the case of the branching Brownian motion.Abstract:
We consider the minimum of a super-critical branching random walk. Addario-Berry and Reed [Ann. Probab. 37 (2009) 1044–1079] proved the tightness of the minimum centered around its mean value. We show that a convergence in law holds, giving the analog of a well-known result of Bramson [Mem. Amer. Math. Soc. 44 (1983) iv+190] in the case of the branching Brownian motion.read more
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References
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An Introduction to Probability Theory and Its Applications.
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Conceptual proofs of L log L criteria for mean behavior of branching processes
TL;DR: The Kesten-Stigum theorem is a fundamental criterion for the rate of growth of a supercritical branching process, showing that an $L \log L$ condition is decisive as mentioned in this paper.
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Postulates for Subadditive Processes
TL;DR: In this paper, the ergodic theory of subadditive processes is examined and a superconvolutive sequence of distributions is introduced, which generalizes the weak law of large numbers.