The longest path in a random graph, Combinatorica, vol.4, issue.1, pp.1-12, 1981. ,
DOI : 10.1007/BF02579172
The asymptotic speed and shape of a particle system, Probability, statistics and analysis, pp.1-23, 1983. ,
DOI : 10.1017/CBO9780511662430.001
On the maximal number of strongly independent vertices in a random acyclic directed graph, SIAM J. Algebraic Discrete Methods, vol.5, issue.4, pp.508-514, 1984. ,
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
The limiting process of $N$-particle branching random walk with polynomial tails, Electronic Journal of Probability, vol.19, issue.0, 2014. ,
DOI : 10.1214/EJP.v19-3111
The first-and last-birth problems for a multitype agedependent branching process Advances in Appl, Probability, vol.8, issue.3, pp.446-459, 1976. ,
Shift in the velocity of a front due to a cutoff, Physical Review E, vol.31, issue.3, pp.2597-2604, 1997. ,
DOI : 10.1002/cpa.3160310502
Abstract, Journal of Applied Probability, vol.9, issue.02, 2016. ,
DOI : 10.1017/CBO9780511662430.001
Community area and food-chain length: theoretical predictions, American Naturalist, pp.1542-1554, 1991. ,
Limit theorems for a random directed slab graph, The Annals of Applied Probability, vol.22, issue.2, pp.702-733, 2012. ,
DOI : 10.1214/11-AAP783
URL : http://doi.org/10.1214/11-aap783
Extended renovation theory and limit theorems for stochastic ordered graphs, Markov Process. Related Fields, vol.9, issue.3, pp.413-468, 2003. ,
Long-range last-passage percolation on the line, The Annals of Applied Probability, vol.24, issue.1, pp.198-234, 2014. ,
DOI : 10.1214/13-AAP920
URL : http://doi.org/10.1214/13-aap920
Stochastic Sequences with a Regenerative Structure that May Depend Both on the Future and on the Past, Advances in Applied Probability, vol.12, issue.04, pp.1083-1110, 2013. ,
DOI : 10.1214/11-AOP678
An approximation of the processing time for a random graph model of parallel computation, Proceedings of 1986 ACM Fall Joint Computer Conference, ACM '86, pp.691-697, 1986. ,
Speed of parallel processing for random task graphs, Communications on Pure and Applied Mathematics, vol.44, issue.3, pp.361-376, 1994. ,
DOI : 10.1007/978-0-387-75953-1
Foundations of modern probability. Probability and its Applications, 2002. ,
Convergence to the Tracy- Widom distribution for longest paths in a directed random graph. ALEA Lat, Am. J. Probab. Math. Stat, vol.10, issue.2, pp.711-730, 2013. ,
A note on branching Lévy processes. Stochastic Process, Appl, vol.82, issue.1, pp.1-14, 1999. ,
DOI : 10.1016/s0304-4149(99)00010-1
URL : https://doi.org/10.1016/s0304-4149(99)00010-1
Speed and fluctuations of N-particle branching Brownian motion with spatial selection, Probability Theory and Related Fields, vol.20, issue.30, 2013. ,
DOI : 10.1016/j.physrep.2003.08.001
$N$-Branching random walk with $\alpha$-stable spine, Teoriya Veroyatnostei i ee Primeneniya, vol.62, issue.2, 2015. ,
DOI : 10.4213/tvp5117
Chain lengths in certain random directed graphs. Random Structures and Algorithms, pp.243-253, 1992. ,
A Stochastic Theory of Community Food Webs IV: Theory of Food Chain Lengths in Large Webs, Proceedings of the Royal Society B: Biological Sciences, vol.228, issue.1252, pp.355-377, 1252. ,
DOI : 10.1098/rspb.1986.0059
Enumerative combinatorics, of cambridge studies in advanced mathematics, 1997. ,
Polynomial Local Improvement Algorithms in Combinatorial Optimization, p.8202049, 1981. ,
Spatial growth of a branching process of particles living in R d, Ann. Probab, vol.10, issue.4, pp.896-918, 1982. ,
-mail address: mallein@math.univ-paris13.fr Sanjay Ramassamy ,