arXiv Analytics

Sign in

arXiv:1101.1810 [math.PR]AbstractReferencesReviewsResources

Convergence in law of the minimum of a branching random walk

Elie Aïdékon

Published 2011-01-10, updated 2013-11-06Version 6

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.

Comments: Published in at http://dx.doi.org/10.1214/12-AOP750 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org) Compared to the published version, we extended our result to the case of an infinite number of children. To this end, we added Corollary 3.5 and slightly changed the proof of Theorem 1.1. arXiv admin note: text overlap with arXiv:1107.2543 by other authors
Journal: Annals of Probability 2013, Vol. 41, No. 3A, 1362-1426
Categories: math.PR
Related articles: Most relevant | Search more
arXiv:math/0310210 [math.PR] (Published 2003-10-15, updated 2006-02-09)
The harmonic explorer and its convergence to SLE(4)
arXiv:1107.2543 [math.PR] (Published 2011-07-13, updated 2015-08-31)
Convergence in law for the branching random walk seen from its tip
arXiv:1205.2682 [math.PR] (Published 2012-05-11, updated 2012-10-05)
Convergence in total variation on Wiener chaos

Links

Toolbox