\begin{thebibliography}{1} \bibitem{BerGou} J.~B\'erard and J.-B. Gou\'er\'e. \newblock {B}runet-{D}errida behavior of branching selection particle systems on the line. \newblock {\em arXiv:0811.2782}, 2008. \bibitem{BruDer1} Eric Brunet and Bernard Derrida. \newblock Shift in the velocity of a front due to a cutoff. \newblock {\em Phys. Rev. E (3)}, 56(3, part A):2597--2604, 1997. \bibitem{BruDer2} {\'E}ric Brunet and Bernard Derrida. \newblock Microscopic models of traveling wave equations. \newblock {\em Computer Physics Communications}, 121-122:376--381, 1999. \bibitem{BruDer3} {\'E}ric Brunet and Bernard Derrida. \newblock Effect of microscopic noise on front propagation. \newblock {\em J. Statist. Phys.}, 103(1-2):269--282, 2001. \bibitem{DerSim1} B.~Derrida and D.~Simon. \newblock The survival probability of a branching random walk in presence of an absorbing wall. \newblock {\em Europhys. Lett. EPL}, 78(6):Art. 60006, 6, 2007. \bibitem{GanHuShi} N.~Gantert, Yueyun Hu, and Zhan Shi. \newblock Asymptotics for the survival probability in a supercritical branching random walk. \newblock {\em arXiv:0811.0262}, 2008. \bibitem{MueMytQua} C.~Mueller, L.~Mytnik, and J.~Quastel. \newblock Small noise asymptotics of traveling waves. \newblock {\em Markov Process. Related Fields}, 14, 2008. \bibitem{DerSim2} Damien Simon and Bernard Derrida. \newblock Quasi-stationary regime of a branching random walk in presence of an absorbing wall. \newblock {\em J. Stat. Phys.}, 131(2):203--233, 2008. \end{thebibliography}