Scaling limit of the path leading to the leftmost particle in a branching random walk
Teoriâ veroâtnostej i ee primeneniâ, Tome 59 (2014) no. 4, pp. 727-751 Cet article a éte moissonné depuis la source Math-Net.Ru

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X. Chen. Scaling limit of the path leading to the leftmost particle in a branching random walk. Teoriâ veroâtnostej i ee primeneniâ, Tome 59 (2014) no. 4, pp. 727-751. http://geodesic.mathdoc.fr/item/TVP_2014_59_4_a4/

[1] Addario-Berry L., Reed B., “Minima in branching random walks”, Ann. Probab., 37:3 (2009), 1044–1079 | DOI

[2] Aïdékon E., Weak convergence of the minimum of a branching random walk, 2011, arXiv: 1101.1810

[3] Aïdékon E., Berestycki J., Brunet É., Shi Z., The branching Brownian motion seen from its tip, 2011, arXiv: 1104.3738v2

[4] Aïdékon E., Shi Z., The Seneta–Heyde scaling for the branching random walk, preprint, 2010

[5] Biggins J. D., Kyprianou A. E., “Fixed points of the smoothing transform: the boundary case”, Electron. J. Probab., 10:17 (2005), 609–631

[6] Caravenna F., “A local limit theorem for random walks conditioned to stay positive”, Probab. Theory Related Fields, 133:4 (2005), 508–530 | DOI

[7] Caravenna F., Chaumont L., “Invariance principles for random walks conditioned to stay positive”, Ann. Inst. Henri Poincaré Probab. Statist., 44:1 (2008), 170–190 | DOI

[8] Chauvin B., Rouault A., “KPP equation and supercritical branching Brownian motion in the subcritical speed area. Application to spatial trees”, Probab. Theory Related Fields, 80:2 (1988), 299–314 | DOI

[9] Durrett R., Iglehart D., Miller D., “Weak convergence to Brownian meander and Brownian excursion”, Ann. Probab., 5:1 (1977), 117–129 | DOI

[10] Feller V., Vvedenie v teoriyu veroyatnostei i ee primeneniya, v. 2, 2-e izd., Mir, M., 1984, 752 pp.

[11] Hu Y., Shi Z., “Minimal position and critical martingale convergence in branching random walks, and directed polymers on disordered trees”, Ann. Probab., 37:2 (2009), 742–789 | DOI

[12] Imhof J.-P., “Density factorizations for Brownian motion, meander and the three-dimensional Bessel process, and applications”, J. Appl. Probab., 21 (1984), 500–510 | DOI

[13] Kozlov M. V., “Ob asimptotike veroyatnosti nevyrozhdeniya kriticheskikh vetvyaschikhsya protsessov v sluchainoi srede”, Teoriya veroyatn. i ee primen., 21:4 (1976), 813–825

[14] Kyprianou A., “Travelling wave solutions to the K-P-P equation: alternatives to Simon Harris' probabilistic analysis”, Ann. Inst. H. Poincaré Probab. Statist., 40:1 (2004), 53–72 | DOI

[15] Lyons R., “A simple path to Biggins' martingale convergence for branching random walk”, Classical and Modern Branching Processes, 84, eds. Athreya K. B., Jagers P., Springer, New York, 1997, 217–221 | DOI

[16] Revuz D., Yor M., Continuous Martingales and Brownian Motion, 3rd ed., Springer-Verlag, New York, 2005, 602 pp.