Fetching the paper…
Reading the bibliography…
We celebrate the 50th anniversary of one the most classical models in probability theory.
Eden, M. A two-dimensional growth process. 1961 Proc. 4th Berkeley Sympos. Math. Statist. and Prob., Vol. IV
1961
Earlier work this paper cites.
Hammersley, J. and Welsh, D. First-passage percolation, subadditive processes, stochastic networks, and generalized renewal theory. 1965 Proc. Internat. Res. Semin., Statist. Lab., Univ. California, Berkeley, Calif
1965
Earlier work this paper cites.
Kingman, J. F. C. (1968). The ergodic theory of sub additive stochastic processes. J. Roy. Statist. Soc. Ser
1968
Earlier work this paper cites.
Hoffman, C. (2008). Geodesics in first passage percolation. Ann. Appl. Probab
1969
Earlier work this paper cites.
Burkholder, D. L. (1973). Discussion of Prof. Kingman’s paper. Annals of Probab
1973
Earlier work this paper cites.
Kingman, J. F. C. (1973). Subadditive Ergodic Theory. Annals of Probab
1973
Earlier work this paper cites.
Richardson, D. (1973). Random growth in a tessellation. Proc. Cambridge Philos. Soc
1973
Earlier work this paper cites.
Gross, L. (1975). Logarithmic Sobolev inequalities. Amer. J. Math
1975
Earlier work this paper cites.
Smythe, R. and Wierman, J. C. (1977). First-Passage Percolation on the Square Lattice. I. Advances in Applied Probability
1977
Earlier work this paper cites.
Benjamini, I. Kalai, G. and Schramm, O. (2003). First passage percolation has sublinear distance variance. Annals of Probab
1978
Earlier work this paper cites.
Smythe, R. and Wierman, J. C. (1978). First-Passage Percolation on the Square Lattice. III. Advances in Applied Probability
1978
Earlier work this paper cites.
Wierman, J. C. and Reh, W. (1978). On conjectures in first passage percolation theory. Annals of Probab
1978
Earlier work this paper cites.
Bollobás, B. (1979). Graph theory. Graduate Texts in Mathematics. Springer- Verlag, New York. An introductory course
1979
Earlier work this paper cites.
Cox, J. T. (1980). The time constant of first-passage percolation on the square lattice. Adv. Appl. Prob
1980
Earlier work this paper cites.
Wierman, J. C., (1980). Weak moment conditions for time coordinates in first-passage percolation models. Journal of Applied Probability
1980
Earlier work this paper cites.
Cox, J. T. and Durrett, R. (1981). Some limit theorems for percolation with necessary and sufficient conditions. Annals of Probab
1981
Earlier work this paper cites.
Cox, J. T. and Kesten, H. (1981). On the continuity of the time constant of first-passage percolation. J. Applied Prob
1981
Earlier work this paper cites.
Durrett, R. and Liggett, T. (1981). The shape of the limit set in Richardson’s growth model. Annals of Probab
1981
Earlier work this paper cites.
Efron, B. and Stein, C. (1981). The jackknife estimate of variance. Annals of Statistics
1981
Earlier work this paper cites.
Rost, H. (1981). Nonequilibrium behaviour of a many particle process: density profile and local equilibria. Z. Wahrsch. Verw. Gebiete
1981
Earlier work this paper cites.
Durrett, R. (1984). Oriented percolation in two dimensions. Annals of Probab
1984
Earlier work this paper cites.
Grimmett, G. and Kesten, H. (1984). First-passage percolation, network flow and electrical resistances Z..Wahrsch. Verw. Gebiete
1984
Earlier work this paper cites.
Busemann, H. The geometry of geodesics
1985
Earlier work this paper cites.
Huse, D. and Henley, C. (1985). Pinning and roughening of domain walls in Ising systems due to random impurities. Phys. Rev. Lett
1985
Earlier work this paper cites.
Huse, D. A., Henley, C. L., Fisher, D. S.: (1985). Huse, Henley, and Fisher respond. Phys. Rev. Lett
1985
Earlier work this paper cites.
Kardar, M. (1985). Roughening by impurities at finite temperatures. Phys. Rev. Lett
1985
Earlier work this paper cites.
Liggett, T. (1985). An Improved Subadditive Ergodic Theorem. Annals of Probab
1985
Earlier work this paper cites.
Chayes, J.T., Chayes, L. and Durrett, R. (1986). Critical behavior of the two-dimensional first passage time. Journal of Stat. Physics
1986
Earlier work this paper cites.
Dhar, D. (1986). Asymptotic shape of Eden clusters, On growth and form. Ed. H. E. Stanley and N. Ostrowsky, Martinus Nijhoff
1986
Earlier work this paper cites.
Kardar, M. and Parisi, G. and Zhang, Y. (1986). Dynamic scaling of growing interfaces. Phys. Rev. Lett
1986
Earlier work this paper cites.
Kesten, H. (1986). Aspects of first passage percolation. École d’Été de Probabilités de Saint Flour XIV,
1986
Earlier work this paper cites.
Steele, J. (1986). An Efron-Stein inequality for nonsymmetric statistics. Annals of Statistics
1986
Earlier work this paper cites.
Zabolitsky, J. G. and Stauffer, D. (1986). Simulation of large Eden clusters. Phys. Rev. A
1986
Earlier work this paper cites.
Chayes, J. T., Chayes, L. and Durrett, R. (1987). Inhomogeneous percolation problems and incipient infinite clusters. J. Phys. A
1987
Earlier work this paper cites.
Kesten, H. (1987). Surfaces with minimal random weight and maximal flows: A higher dimensional version of first passage percolation, Illinois J. Math
1987
Earlier work this paper cites.
Krug, J. (1987). Scaling relation for a growing surface. Phys. Rev. A
1987
Earlier work this paper cites.
Wehr, J. and Aizenman, M. (1987). Fluctuations of extensive functions of quenched random couplings. J. Stat. Phys
1987
Earlier work this paper cites.
Wolf, D. E. and Kertesz, J. (1987). Noise reduction in Eden models: I. J. Phys. A
1987
Earlier work this paper cites.
Burton, R.M. and Keane, M. (1989). Density and uniqueness in percolation. Comm. Math. Phys
1989
Earlier work this paper cites.
Boivin, D. (1990). First passage percolation: the stationary case. Probab. Theory Relat. Fields
1990
Earlier work this paper cites.
Grimmett, G. and Marstrand, J. M. (1990). The supercritical phase of percolation is well behaved. Proc. Roy. Soc. London Ser. A
1990
Earlier work this paper cites.
Burrows, E.M. (1991). Seaweeds of the British Isles. London: Natural History Museum
1991
Earlier work this paper cites.
Chayes, L. (1991). On the critical behavior of the first passage time in d ≥ 3 d\geq 3 . Helvetica Phys. Acta
1991
Earlier work this paper cites.
Derrida, B. and Dickman, R. (1991). On the interface between two growing Eden clusters. Journal of Physics A: Mathematical and General
1991
Earlier work this paper cites.
Forgacs, G., Lipowsky R. and Nieuwenhuizen, T. (1991). The behavior of interfaces in ordered and disordered systems. In Phase transitions and critical phenomena
1991
Earlier work this paper cites.
Krug, J. and Spohn, H. Kinetic roughening of growing interfaces. in Solids far from equilibrium. Edited by C. Godrèche. Collection Aléa-Saclay: Monographs and Texts in Statistical Physics, 1. Cambridge University Press, Cambridge,
1992
Earlier work this paper cites.
Alexander, K. (1993). A Note on Some Rates of Convergence in First-Passage Percolation. Ann. Appl. Probab
1993
Earlier work this paper cites.
Chayes, L. and Winfield, C. (1993). The density of interfaces: A new first passage problem. J. Appl. Prob
1993
Earlier work this paper cites.
Fontes, L. and Newman, C.M. (1993). First passage percolation for random colorings of ℤ d {\mathbb{Z}}^{d} . Ann. Appl. Probab
1993
Earlier work this paper cites.
Kesten, H. (1993). On the speed of convergence in first-passage percolation. Ann. Appl. Probab
1993
Earlier work this paper cites.
Pemantle, R. and Peres, Y. (1994). Planar first-passage percolation times are not tight. Probability and phase transition (Cambridge, 1993)
1993
Earlier work this paper cites.
Van den Berg, J. and Kesten, H. (1993). Inequalities for the time constant in first-passage percolation. Ann. Appl. Probab
1993
Earlier work this paper cites.
Talagrand, M. (1994). On Russo’s approximate zero-one law. Annals of Probab
1994
Earlier work this paper cites.
Tracy, C. A.; Widom, H. (1994). Level-spacing distributions and the Airy kernel, Comm. in Math. Phys
1994
Earlier work this paper cites.
Häggström, O. and Meester, R. (1995). Asymptotic shapes for stationary first passage percolation. Annals of Probab
1995
Earlier work this paper cites.
Newman, C. M. A surface view of first-passage percolation. Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994), 1017–1023, Birkhäuser, Basel, 1995
1995
Earlier work this paper cites.
Newman, C. M. and Piza, M. (1995). Divergence of shape fluctuations in two dimensions. Annals of Probab
1995
Earlier work this paper cites.
Rhee, W. (1995). On Rates of Convergence for Common Subsequences and First Passage Time. Ann. Appl. Probab
1995
Cited alongside, same era.
Talagrand, M. (1995). Concentration of measure and isoperimetric inequalities in product spaces. Publ. Math. I.H.E.S
1995
Cited alongside, same era.
Zhang, Y. (1995). Supercritical behaviors in first-passage percolation. Stochastic Proc. Appl
1995
Cited alongside, same era.
Antal, P. and Pisztora, A. (1996). On the chemical distance for supercritical Bernoulli percolation. Annals of Probab
1996
Cited alongside, same era.
Kesten, H. and Zhang, Y. (1996). A central limit theorem for critical first-passage percolation in two dimensions. Probab. Theory Relat. Fields
1996
Cited alongside, same era.
Garet, O. (2009). Capacitive Flows on a 2D random net. Ann. of Appl. Probab
2009
Later among the works it cites.
Seppäläinen, T. (2009). Lecture Notes on the Corner Growth Model. http://www.math.wisc.edu/ seppalai/cornergrowth-book/ajo.pdf
2009
Later among the works it cites.
Anderson, G., Guionnet, A. and Zeitouni, O. (2010) An introduction to random matrices
2010
Later among the works it cites.
Blair-Stahn, N. D. (2010). First passage percolation and competition models. arXiv:1005.0649
2010
Later among the works it cites.
Bjorklund, M. (2010). The asymptotic shape theorem for generalized first passage percolation. Annals of Probab
2010
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Licea, C. and Newman, C. M. (1996). Geodesics in two-dimensional first-passage percolation. Annals of Probab
1996
Cited alongside, same era.
Licea, C. and Newman, C. and Piza, M. (1996). Superdiffusivity in first-passage percolation. Probab. Theory Related Fields
1996
Cited alongside, same era.
Aizenman, M. (1997). On the Number of Incipient Spanning Clusters. Nuclear Physics B
1997
Cited alongside, same era.
Alexander, K. (1997). Approximation of subadditive functions and convergence rates in limiting-shape results. Annals of Probab
1997
Cited alongside, same era.
Newman, C. M. Topics in disordered systems. Springer, 1997
1997
Cited alongside, same era.
Wehr, J. (1997). On the number of infinite geodesics and ground states in disordered systems. J. Statist. Phys
1997
Cited alongside, same era.
Alm, S. E. (1998). A Note on a Problem by Welsh in First-Passage Percolation. Combin. Probab. Comput
1998
Cited alongside, same era.
Lions, P.-L. and P. E. Souganidis. (2010). Stochastic homogenization of Hamilton-Jacobi and viscous Hamilton-Jacobi equations with convex nonlinearities - revisited. Communications in Mathematical Sciences
2010
Later among the works it cites.
Rossignol, R. and Théret. (2010). Law of large numbers for the maximal flow through tilted cylinders in two-dimensional first passage percolation. Stoch. Proc. Appl.,
2010
Later among the works it cites.
Zhang, Y. (2010). On the concentration and the convergence rate with a moment condition in first-passage percolation. Stoch. Proc. Appl
2010
Later among the works it cites.
Alexander, K. (2011). Subgaussian rates of convergence of means in directed first passage percolation. arXiv: 1101.1549
2011
Later among the works it cites.
Auffinger, A. and Louidor, O. (2011). Directed polymers in random environment with heavy tails. Comm. on Pure and Applied Mathematics
2011
Later among the works it cites.
Cerf, R. and Théret, M. (2011). Law of the large numbers for the maximal flow through a domain of ℝ d \mathbb{R}^{d} in first passage percolation. Trans. Amer. Math. Soc
2011
Later among the works it cites.
Cerf, R. and Théret, M. (2011). Lower large deviations for the maximal flow through a domain of ℝ d \mathbb{R}^{d} in first passage percolation. Probab. Theory and Relat. Fields
2011
Later among the works it cites.
Coupier, D. (2011). Multiple geodesics with the same direction. Elect. Com. Probab
2011
Later among the works it cites.
Couronné, O., Enriquez, N. and Gerin, L. (2011) Construction of a short path in high-dimensional first passage percolation. Elect. Comm. in Probab
2011
Later among the works it cites.
Kuhr, J.-T., Leisner, M. and Frey, E. (2011). Range expansion with mutation and selection: dynamical phase transition in a two-species Eden model. New Journal of Physics
2011
Later among the works it cites.
Mourrat, J.-C. (2012). Lyapunov exponents, shape theorems and large deviations for the random walk in random potential ALEA, Lat. Am. J. Probab. Math. Stat
2012
Later among the works it cites.
Van den Berg, J. and Kiss, D. (2012). Sublinearity of the travel-time variance for dependent first-passage percolation. Annals of Probab
2012
Later among the works it cites.
Ahlberg, D. (2013). Convergence towards an asymptotic shape in first-passage percolation on cone-like subgraphs of the integer lattice. To appear in J. Theoret. Probab
2013
Later among the works it cites.
2013
Later among the works it cites.
Alexander, K. and Zygouras, N. (2013). Subgaussian concentration and rates of convergence in directed polymers. Electronic Journal of Probability
2013
Later among the works it cites.
Auffinger, A. and Damron, M. (2013). The universal scaling relation for polymers in a random environment and related models ALEA, Lat. Am. J. Probab. Math. Stat
2013
Later among the works it cites.
Auffinger, A. and Damron, M. (2013). Differentiability at the edge of the limit shape and related results in first passage percoaltion. Probab. Theory and Rel. Fields
2013
Later among the works it cites.
Auffinger, A., Damron, M. and Hanson, J. (2013). Limiting geodesics for first-passage percolation on subsets of ℤ 2 {\mathbb{Z}}^{2} , To appear in Annals of Applied Probability
2013
Later among the works it cites.
Basdevant, A. Enriquez, N., Gerin, L. (2013). Distances in the highly supercritical percolation cluster. Annals of Probab
2013
Later among the works it cites.
Boucheron, S, Lugosi, G., and Massart, P. Concentration inequalities. A nonasymptotic theory of independence. With a foreword by Michel Ledoux. Oxford University Press, Oxford
2013
Later among the works it cites.
Chatterjee, S. (2013). The universal relation between scaling exponents in first-passage percolation. Ann. of Math. (2)
2013
Later among the works it cites.
Damron, M. and Hochman, M. (2013) Examples of non-polygonal limit shapes in i.i.d. first-passage percolation and infinite coexistence in spatial growth models. Annals of Applied Probability
2013
Later among the works it cites.
Garet, O., Gouere, J-B. and Marchand, R. (2013). The number of open paths in oriented percolation. arXiv:1312:2571
2013
Later among the works it cites.
2013
Later among the works it cites.
Hanson, J. (2013). Ph.D. thesis
2013
Later among the works it cites.
2013
Later among the works it cites.
Krishnan, A. (2013). Ph.D. Thesis
2013
Later among the works it cites.
2013
Later among the works it cites.
Rossignol, R. and Théret. (2013). Lower large deviations for the maximal flow through tilted cylinders in two-dimensional first passage percolation. ESAIM: Probability and Statistics,
2013
Later among the works it cites.
Timár, A. (2013). Boundary-connectivity via graph theory. Proceedings of the AMS
2013
Later among the works it cites.
2014
Later among the works it cites.
Auffinger, A. and Damron, M. (2014). A simplified proof of the relation between scaling exponents in first-passage percolation. Annals of Probab
2014
Later among the works it cites.
Auffinger, A., Damron, M. and Hanson, J. (2014). Rate of convergence of the mean for sub-additive ergodic sequences. To appear at Adv. in Math
2014
Later among the works it cites.
Basdevant, A. Enriquez, N., Gerin, L., Gouéré, J.-B. (2014). The shape of large balls in highly supercritical percolation. Elect. Journal Probab
2014
Later among the works it cites.
2014
Later among the works it cites.
2014
Later among the works it cites.
Damron, M. and Hanson, J. (2014). Busemann functions and infinite geodesics in two-dimensional first-passage percolation. Comm. Math. Phys
2014
Later among the works it cites.
2014
Later among the works it cites.
Garet, O. and Marchand, R. (2014). Large deviations for the contact process in random environment. Annals of Probab
2014
Later among the works it cites.
Sodin, S. (2014). Positive temperature versions of two theorems on first-passage percolation. Geometric Aspects of Functional Analysis
2014
Later among the works it cites.
2014
Later among the works it cites.
Van der Hofstad, R. (2014). Random Graphs and Complex Networks. Vol. II. Online at http://www.win.tue.nl/~rhofstad/NotesRGCNII.pdf
2014
Later among the works it cites.
Yao, C.-L. (2014). Law of large numbers for critical first-passage percolation on the triangular lattice. Electronic Communications in Probability
2014
Later among the works it cites.
Antunovic, T. and Procaccia, E. (2015). Stationary Eden model on groups. arXiv 1410.4944
2015
Closest in time.
Damron, M. and Hanson, J. (2015). Bigeodesics in first-passage percolation. In preparation
2015
Closest in time.
2015
Closest in time.
2015
Closest in time.
2015
Closest in time.
Yao, C.-L. (2015). Limit theorems for critical first-passage percolation on the triangular lattice. arXiv: 1602.00065
2015
Closest in time.
Cerf, R. and Théret, M. (2011). Upper large deviations for the maximal flow through a domain of ℝ d \mathbb{R}^{d} in first passage percolation. Ann. of Appl. Probab
2075
Closest in time.
Kardar, M. and Zhang, Y.-C. (1987). Scaling of directed polymers in random media. Phys. Rev. Lett
2090
Closest in time.