Minima in branching random walks
Addario-Berry, Louigi ; Reed, Bruce
Ann. Probab., Tome 37 (2009) no. 1, p. 1044-1079 / Harvested from Project Euclid
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Given a branching random walk, let Mn be the minimum position of any member of the nth generation. We calculate EMn to within O(1) and prove exponential tail bounds for P{|Mn−EMn|>x}, under quite general conditions on the branching random walk. In particular, together with work by Bramson [Z. Wahrsch. Verw. Gebiete 45 (1978) 89–108], our results fully characterize the possible behavior of EMn when the branching random walk has bounded branching and step size.
Publié le : 2009-05-15
Classification:  Branching random walks,  branching processes,  random trees,  60J80,  60G50 
@article{1245434028,
     author = {Addario-Berry, Louigi and Reed, Bruce},
     title = {Minima in branching random walks},
     journal = {Ann. Probab.},
     volume = {37},
     number = {1},
     year = {2009},
     pages = { 1044-1079},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1245434028}
}

Addario-Berry, Louigi; Reed, Bruce. Minima in branching random walks. Ann. Probab., Tome 37 (2009) no. 1, pp.  1044-1079. http://gdmltest.u-ga.fr/item/1245434028/