Fetching the paper…
Reading the bibliography…
Convergence of directed forests, spanning on random subsets of lattices or on point processes, towards the Brownian web has made the subject of an abundant literature, a large part of which relies on a criterion proposed by Fontes, Isopi, Newman and Ravishankar (2004).
A. E. Scheidegger, “A stochastic model for drainage pattern into an intramontane trench”, Bull. Ass. Sci. Hydrol. , 12
1967
Earlier work this paper cites.
A. D. Howard, “Simulation of stream networks by headward growth and branching”, Geogr. Anal
1971
Earlier work this paper cites.
R. Arratia, “Coalescing Brownian motions on the line”, Ph.D. thesis, University of Wisconsin, Madison, 1979
1979
Earlier work this paper cites.
P. Billingsley, “Probability and measure”, Second Edition., John Wiley and Sons, 1986
1986
Earlier work this paper cites.
S. P. Meyn and R. L. Tweedie, “Markov chains and stochastic stability”, Springer-Verlag, London, 1993
1993
Earlier work this paper cites.
S. P. Meyn and R. L. Tweedie, “Stability of Markovian processes III: Foster-Lyapunov criteria for continuous-time processes”, Advances in Applied Probability
1993
Earlier work this paper cites.
I. Rodriguez-Iturbe and A. Rinaldo, “Fractal river basins: chance and self-organization”, Cambridge University Press, New York (1997)
1997
Earlier work this paper cites.
B. Tóth and W. Werner, “The true self-repelling motion”, Probab. Theory Related Fields
1998
Earlier work this paper cites.
L. R. G. Fontes, M. Isopi, C. M. Newman and K. Ravishankar, “The Brownian web: characterization and convergence”, Ann. Probab
2004
Earlier work this paper cites.
P. Ferrari, C. Landim and H. Thorisson, “Poisson trees, succession lines and coalescing random walks”, Ann. Inst. H. Poincaré Probab. Statist
2004
Cited alongside, same era.
S. Gangopadhyay, R. Roy and A. Sarkar, “Random oriented trees: a model of drainage networks”, Ann. Appl. Probab
2004
Cited alongside, same era.
P. A. Ferrari, L. R. G. Fontes and X. Y. Wu, “Two-dimensional Poisson Trees converge to the Brownian web”, Ann. Inst. H. Poincaré Probab. Statist
2005
Cited alongside, same era.
C. M. Newman, K. Ravishankar and R. Sun, “Convergence of coalescing nonsimple random walks to the Brownian web”, Electron. J. Prob
2005
Cited alongside, same era.
R. Roy, K. Saha, and A. Sarkar, “Random directed forest and the Brownian web”, Ann. Inst. H. Poincaré Probab. Statist. , 52
2005
Cited alongside, same era.
D. Coupier, V.C. Tran, “The 2d-directed spanning forest is almost surely a tree”, Random Structures and Algorithms
2013
Later among the works it cites.
A. Sarkar and R. Sun, “Brownian web in the scaling limit of supercritical oriented percolation in dimension 1 + 1 1+1 ”, Electron. J. of Probab. , 18
2013
Later among the works it cites.
C. Coletti and G. Valle, “Convergence to the Brownian web for a generalization of the drainage network model”, Ann. Inst. H. Poincaré Probab. Statist
2014
Later among the works it cites.
N. Berestycki, C. Garban and A. Sen, “Coalescing Brownian flows: a new approach”. Ann. Probab
2015
Closest in time.
A. Sturm and J.M. Swart, “A particle system with cooperative branching and coalescence”, Ann. of Appl. Probab. , 15
2015
Closest in time.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
F. Baccelli and C. Bordenave, “The radial spanning tree of a Poisson point process” Ann. Appl. Probab
2007
Cited alongside, same era.
R. Sun and J. Swart, “The Brownian net”, Ann. Probab
2008
Cited alongside, same era.
C.-F. Coletti, E. S. Dias and L. R. G. Fontes, “Scaling limit for a drainage network model”, J. Appl. Probab
2009
Cited alongside, same era.
S.N. Ethier and T.G. Kurtz, “Markov Processes: Characterization and Convergence”, Wiley, 2009
2009
Cited alongside, same era.
R. Roy, K. Saha, and A. Sarkar, “Hack’s law in a drainage network model: a Brownian web approach”, Ann Appl. Probab. , 26
2016
Closest in time.
E. Schertzer, R. Sun, and J. Swart, “The Brownian web, the Brownian net, and their universality”, Advances in Disordered Systems, Random Processes and Some Applications , 270–368, Cambridge University Press, 2017
2017
Closest in time.
2017
Closest in time.