Inhomogeneous Long-Range Percolation on the Hierarchical Lattice
Tài liệu tham khảo
Bollobás, 2006
Grimmett, 1999
Schulman, 1983, Long range percolation in one dimension, J. Phys. A: Math. Gen., 16, L639, 10.1088/0305-4470/16/17/001
Aizenman, 1986, Discontinuity of the percolation density in one-dimensional 1/|x - y|2 percolation models, Commun. Math. Phys., 107, 611, 10.1007/BF01205489
Berger, 2002, Transience, recurrence and critical behavior for long-range percolation, Commun. Math. Phys., 226, 531, 10.1007/s002200200617
Biskup, 2004, On the scaling of chemical distance in long-range percoaltion models, Ann. Probab., 32, 2938, 10.1214/009117904000000577
Biskup, 2011, Graph diameter in long-range percolation, Rand. Struct. Alg., 39, 210, 10.1002/rsa.20349
Coppersmith, 2002, The diameter of a long-range percolation graph, Random Struct. Alg., 21, 1, 10.1002/rsa.10042
Trapman, 2010, The growth of the infinite long-range percolation cluster, Ann. Probab., 38, 1583, 10.1214/09-AOP517
Janson, 2000
Bollobás, 2007, The phase transition in inhomogeneous random graphs, Rand. Struct. Alg., 31, 3, 10.1002/rsa.20168
Britton, 2006, Generating simple random graphs with prescribed degree distribution, J. Stat. Phys., 124, 1377, 10.1007/s10955-006-9168-x
Deijfen, 2009, Random intersection graphs with tunable degree distribution and clustering, Probab. Eng. Inform. Sc., 23, 661, 10.1017/S0269964809990064
Shang, 2010, Degree distributions in general random intersection graphs, Electron. J. Combin., 17, R23, 10.37236/295
Janson, 2010, Large cliques in a power-law random graph, J. Appl. Prob., 47, 1124, 10.1017/S0021900200007415
Shang, 2012, Multi-type directed scale-free percolation, Commun. Theor. Phys., 57, 701, 10.1088/0253-6102/57/4/26
Shang, 2013, Large dicliques in a directed inhomogeneous random graph, Int. J. Comput. Math., 90, 445, 10.1080/00207160.2012.735663
Barabási, 2003, Hierarchical organization in complex networks, Phys. Rev. E, 67, 026112, 10.1103/PhysRevE.67.026112
Rammal, 1986, Ultrametricity for physicists, Rev. Mod. Phys., 58, 765, 10.1103/RevModPhys.58.765
Athreya, 2010, Survival of contact processes on the hierarchical group, Probab. Theory Relat. Fields, 147, 529, 10.1007/s00440-009-0214-x
Dawson, 2013, Percolation in an ultrametric space, Electron. J. Probab., 18, 13, 10.1214/EJP.v18-1789
Dawson, 2007, Percolation in a hierarchical random graph, Commun. Stochastic Analysis, 1, 29, 10.31390/cosa.1.1.04
Koval, 2012, Long-range percolation on the hierarchical lattice, Electron. J. Probab., 17, 57, 10.1214/EJP.v17-1977
Shang, 2012, Percolation in a hierarchical lattice, Z. Naturforsch. A, 67, 225, 10.5560/zna.2012-0012
Shang, 2013, Phase transition in long-range percolation on bipartite hierarchical lattices, The Scientific World J., 2013, 172393, 10.1155/2013/172393
Schneider, 2002
Gandolfi, 1992, Uniqueness of the infinite component in a random graph with applications to percolation and spin glasses, Probab. Theory Related Fields, 92, 511, 10.1007/BF01274266