Chế độ gần như ổn định của một quá trình đi bộ phân nhánh trong sự xuất hiện của một bức tường hấp thụ

Antal, T., Blagoev, K.B., Trugman, S.A., Redner, S.: Aging and immortality in a cell proliferation model. J. Theor. Biol. 248, 411–417 (2007) Assaf, M., Meerson, B.: Spectral theory of metastability and extinction in birth-death systems. Phys. Rev. Lett. 97, 200602 (2006) Berestycki, H., Hamel, F., Nadirashvili, N.: Propagation speed for reaction-diffusion equations in general domains. C. R. Acad. Sci. Paris 339, 163–168 (2004) Berestycki, H., Hamel, F., Roques, L.: Analysis of the periodically fragmented environment model: I—Species persistence. J. Math. Biol. 51, 75–113 (2005) Bramson, M.: Convergence of solutions of the Kolmogorov equation to traveling waves. Mem. Am. Math. Soc. 44, 1–190 (1983) Brunet, É., Derrida, B.: Exactly soluble noisy traveling-wave equation appearing in the problem of directed polymers in a random medium. Phys. Rev. E 70, 016106 (2004) Brunet, É., Derrida, B., Mueller, A., Munier, S.: Noisy traveling waves: Effect of selection on genealogies. Europhys. Lett. 76, 1–7 (2006) Brunet, É., Derrida, B., Mueller, A., Munier, S.: Phenomenological theory giving the full statistics of the position of fluctuating pulled fronts. Phys. Rev. E 73, 056126 (2006) Brunet, É., Derrida, B., Mueller, A., Munier, S.: Effect of selection on ancestry: an exactly soluble case and its phenomenological generalization. Phys. Rev. E 76, 041104 (2007). cond-mat:0704.3389 Cattiaux, P., Collet, P., Lambert, A., Martinez, S., Méléard, S., San Martin, J.: Quasi-stationary distributions and diffusion models in population dynamics. http://arxiv.org/abs/math/0703781 (2007) de Oliveira, M.M., Dickman, R.: How to simulate the quasistationary state. Phys. Rev. E 71, 016129 (2005) Derrida, B., Simon, D.: The survival probability of a branching random walk in presence of an absorbing wall. Europhys. Lett. 78, 60006 (2007) Dickman, R., Vidigal, R.: Quasi-stationary distributions for stochastic processes with an absorbing state. J. Phys. A Math. Gen. 35, 1147–1166 (2002) Doering, C.R., Mueller, C., Smereka, P.: Interacting particles, the stochastic Fisher-Kolmogorov-Petrovsky-Piscounov equation, and duality. Phys. A 325, 243–259 (2003) Domany, E., Kinzel, W.: Directed percolation in two dimensions: numerical analysis and an exact solution. Phys. Rev. Lett. 47, 5–8 (1981) Dubertret, B., Liu, S., Ouyang, Q., Libchaber, A.: Dynamics of DNA-protein interaction deduced from in vitro DNA evolution. Phys. Rev. Lett. 86, 6022–6025 (2001) Escudero, C.: Field theory of propagating reaction-diffusion fronts. Phys. Rev. E 70, 041102 (2004) Ferrari, P.A., Martinez, S., San Martín, J.: Phase transition for absorbed Brownian motion with drift. J. Stat. Phys. 86, 213–231 (1997) Fisher, R.: The wave of advance of advantageous genes. Ann. Eugen. 7, 355 (1937) Hallatschek, O., Nelson, D.: Gene surfing in expanding populations. Theor. Popul. Biol. 73, 158 (2008). arXiv:q-bio/0703040 Hardy, R., Harris, S.: A new formulation of the spine approach to branching diffusions. Mathematics Preprint, University of Bath, no. 0404 (2004) Harris, J., Harris, S.: Survival probabilities for branching Brownian motion with absorption. Electron. Commun. Probab. 12, 81–92 (2007) Harris, T.: The Theory of Branching Processes. Springer, Berlin (1962) Hinrichsen, H.: Nonequilibrium critical phenomena and phase transitions into absorbing states. Adv. Phys. 49, 815 (2000) Iancu, E., Mueller, A., Munier, S.: Universal behavior of QCD amplitudes at high energy from general tools of statistical physics. Phys. Lett. B 606, 342–350 (2005) Kang, K., Redner, S.: Fluctuation-dominated kinetics in diffusion-controlled reactions. Phys. Rev. A 32, 435–447 (1985) Kesten, H., Ney, P., Spitzer, F.: The Galton-Watson process with mean one and finite variance. Theory Probab. Appl. 11, 513–540 (1966) Khalili-Françon, E.: Processus de Galton-Watson. Lect. Notes Math. 321, 122–135 (1973) Kloster, M.: Analysis of evolution through competitive selection. Phys. Rev. Lett. 95, 168701 (2005) Marquet, C., Peschanski, R., Soyez, G.: Traveling waves and geometric scaling at nonzero momentum transfer. Nucl. Phys. A 756, 399–418 (2005) McKean, H.: Application of Brownian motion to the equation of Kolmogorov-Petrovskii-Piskunov. Commun. Pure Appl. Math. 28, 323–331 (1975) Moro, E.: Hybrid method for simulating front propagation in reaction-diffusion systems. Phys. Rev. E 69, 060101(R) (2004) Mueller, C., Mytnik, L., Quastel, J.: The asymptotic speed of a random traveling wave. Preprint (2008) Mueller, C., Sowers, R.: Random traveling waves for the KPP equation with noise. J. Funct. Anal. 128, 439–498 (1995) Munier, S., Peschanski, R.: Geometric scaling as traveling waves. Phys. Rev. Lett. 91, 232001 (2003) Odor, G.: Universality classes in nonequilibrium lattice systems. Rev. Mod. Phys. 76, 663–724 (2004) Panja, D.: Effects of fluctuations on propagating fronts. Phys. Rep. 393, 87–174 (2004) Pechenik, L., Levine, H.: Interfacial velocity corrections due to multiplicative noise. Phys. Rev. E 59, 3893–3900 (1999) Peliti, L.: In: Lectures at the Summer College on Frustrated Systems (1997). cond-mat/9712027 Slack, R.S.: A branching process with mean one and possibly infinite variance. Probab. Theory Relat. Fields 9, 139–145 (1968) Snyder, R.: How demographic stochasticity can slow biological invasions. Ecology 84, 1333–1339 (2003) Steinsaltz, D., Evans, S.: Quasistationary distributions for one-dimensional diffusions with killing. Am. Math. Soc. 359, 1285–1324 (2005) van Saarloos, W.: Front propagation into unstable states. Phys. Rep. 386, 29–222 (2003) Wegner, F.: In: Domb, C., Green, M.S. (eds.) Phase Transitions and Critical Phenomena, vol. 6. Academic Press, San Diego (1976) Yaglom, M.: Certain limit theorems of the theory of branching random processes. Rep. Acad. Sci. USSR 56, 795–798 (1947)