E. A¨?dékona¨?dékon and B. Jaffuel, Survival of branching random walks with absorption. Stochastic Process, Appl, vol.121, issue.9, pp.1901-1937, 2011.

J. Bérard and J. Gouéré, Brunet-Derrida Behavior of Branching-Selection Particle Systems on the Line, Communications in Mathematical Physics, vol.131, issue.2, pp.323-342, 2010.
DOI : 10.1007/s00220-010-1067-y

J. Bérard and P. Maillard, The limiting process of N -particle branching random walk with polynomial tails Electron, J. Probab, vol.19, issue.17, 2014.

J. D. Biggins, Branching out, Probability and mathematical genetics, pp.113-134, 2010.
DOI : 10.1017/CBO9781139107174.007

J. D. Biggins and A. E. Kyprianou, Measure change in multitype branching, Advances in Applied Probability, vol.64, issue.02, pp.544-581, 2004.
DOI : 10.1214/aop/1024404291

J. D. Biggins, A. E. Kyprianou, ´. E. Brunet, and B. Derrida, Fixed Points of the Smoothing Transform: the Boundary Case, Electronic Journal of Probability, vol.10, issue.0, pp.609-631, 1997.
DOI : 10.1214/EJP.v10-255

´. E. Brunet, B. Derrida, A. H. Mueller, and S. Munier, Effect of selection on ancestry: An exactly soluble case and its phenomenological generalization, Physical Review E, vol.76, issue.4, p.41104, 2007.
DOI : 10.1103/PhysRevE.76.041104

W. Feller, An introduction to probability theory and its applications, 1971.

K. Fleischmann and V. Wachtel, Lower deviation probabilities for supercritical Galton???Watson processes???, Annales de l'Institut Henri Poincare (B) Probability and Statistics, vol.43, issue.2, pp.233-255, 2007.
DOI : 10.1016/j.anihpb.2006.03.001

N. Gantert, Y. Hu, and Z. Shi, Asymptotics for the survival probability in a killed branching random walk, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.47, issue.1, pp.111-129, 2011.
DOI : 10.1214/10-AIHP362

URL : https://hal.archives-ouvertes.fr/hal-00579979

J. Kahane and J. Peyrì-ere, Sur certaines martingales de Benoit Mandelbrot, Advances in Mathematics, vol.22, issue.2, pp.131-145, 1976.
DOI : 10.1016/0001-8708(76)90151-1

R. Lyons, A Simple Path to Biggins??? Martingale Convergence for Branching Random Walk, Classical and modern branching processes, pp.217-221, 1994.
DOI : 10.1007/978-1-4612-1862-3_17

R. Lyons, R. Pemantle, and Y. Peres, Conceptual Proofs of $L$ Log $L$ Criteria for Mean Behavior of Branching Processes, The Annals of Probability, vol.23, issue.3, pp.1125-1138, 1995.
DOI : 10.1214/aop/1176988176

B. Mallein, Branching random walk with selection at critical rate, Bernoulli, vol.23, issue.3, 2015.
DOI : 10.3150/15-BEJ796

URL : https://hal.archives-ouvertes.fr/hal-01322449

R. Pemantle, Search cost for a nearly optimal path in a binary tree, The Annals of Applied Probability, vol.19, issue.4, pp.1273-1291, 2009.
DOI : 10.1214/08-AAP585

J. Peyrì-ere, Turbulence et dimension de Hausdorff, C. R. Acad. Sci. Paris Sér. A, vol.278, pp.567-569, 1974.

Y. V. Prohorov, Convergence of random processes and limit theorems in probability theory, Teor. Veroyatnost. i Primenen, vol.1, pp.177-238, 1956.