Randomly generated groups (Chapter 5) - Surveys in Combinatorics 2015

[1] S., Antoniuk, E., Friedgut, T., Łuczak, A sharp threshold for collapse of the random triangular group, arXiv:1403.3516.

[2] S., Antoniuk, T., Łuczak, T., Prytula, P., Przytycki, B., Zalewski, When a random triangular group is free?, in preparation.

[3] S., Antoniuk, T., Łuczak, J., Świątkowski, Collapse of random triangular groups: a closer look, Bull. Lond. Math. Soc. 46 (2014), 761–764.

[4] S., Antoniuk, T., Łuczak, J., Świątkowski, Random triangular groups at density 1/3, Compositio Mathematica 151 (2015), 167–178.Google Scholar

[5] L., Aronshtam, N., Linial, The threshold for collapsibility in random complexes, Random Structures & Algorithms, to appear.

[6] L., Aronshtam, N., Linial, When does the top homology of a random simplicial complex vanish?, Random Structures & Algorithms 46 (2015), 26–35.Google Scholar

[7] L., Aronshtam, N., Linial, T., Łuczak, R., Meshulam, Collapsibility and vanishing of top homology in random simplicial complexes, Discrete Comput. Geom. 49 (2013), 317–334.Google Scholar

[8] E., Babson, C., Hoffman, M., Kahle, The fundamental group of random 2-complexes, J. Amer. Math. Soc. 24 (2011), 1–28.

[9] S. R., Blackburn, P. M., Neumann, G., Venkataraman, “Enumeration of finite groups”. Cambridge Tracts in Mathematics, 173. Cambridge University Press, Cambridge, 2007.

[10] B., Bollobás, The evolution of random graphs, Trans. Amer. Math. Soc. 286 (1984), 257–274.

[11] B., Bollobás, A., Thomason, Threshold functions, Combinatorica 7 (1987), 35–38.Google Scholar

[12] P.J., Cameron, The random graph revisited, European Congress of Mathematics, Vol. I (Barcelona, 2000), 267–274, Progr. Math., 201, Birkhäuser, Basel, 2001.Google Scholar

[13] B., DeMarco, A., Hamm, J., Kahn, On the triangle space of a random graph, J. Combin. 4 (2013), 229–249.

[14] J. D., Dixon, The probability of generating the symmetric group, Math. Z. 110 (1969), 199–205.

[15] P., Erdős, A., Rényi, On the evolution of random graphs, Magyar Tud. Akad. Mat. Kutató Int. Közl. 5 (1960), 17–61.

[16] E., Friedgut, Sharp thresholds of graph properties, and the k-sat problem. With an appendix by Jean Bourgain. J. Amer. Math. Soc. 12 (1999), 1017–1054.

[17] G., Grimmett, S., Janson; Random even graphs. Electron. J. Combin. 16 (2009), no. 1, Research Paper, 46, 19 pp.Google Scholar

[18] M., Gromov, Asymptotic invariants of infinite groups. Geometric Group Theory, London Math. Soc. Lecture Note Ser. 182 (1993), 1–295.Google Scholar

[19] P., Heinig, T., Łuczak, Hamiltonian space of random graphs, in preparation.

[20] C., Hoffman, M., Kahle, E., Paquette, Spectral gaps of random graphs and applications to random topology, arXiv:1201.0425.

[21] S., Janson, T., Łuczak, A., Ruciński, “Random Graphs”, Wiley, New York, 2000.

[22] M., Kahle, Topology of random simplicial complexes: a survey. To appear in AMS Contemporary Volumes in Mathematics, Nov 2014, arXiv:1301.7165.Google Scholar

[23] M., Kotowski, M., Kotowski, Random groups and property (T): Żuk's theorem revisited, J. London Math. Soc. 88 (2013), 396–416.

[24] N., Linial, R., Meshulam, Homological connectivity of random 2- complexes, Combinatorica 26 (2006), 475–487.Google Scholar

[25] N., Linial, Y., Peled, On the phase transition in random simplicial complexes, arXiv:1410.1281.

[26] T., Łuczak, The automorphisms group of random graphs with given number of edges, Math. Proc. Camb. Phil. Soc. 104 (1988), 441–449.

[27] T., Łuczak, Components behavior near the critical point of the random graph process, Random Structures … Algorithms 1 (1990), 287–310.Google Scholar

[28] T., Łuczak, Cycles in a random graph near the critical point, Random Structures & Algorithms 2 (1991), 421–440.Google Scholar

[29] T., Łuczak, Size and connectivity of the k-core of a random graph, Discrete Math. 91 (1991), 61–68.Google Scholar

[30] T., Łuczak, How to deal with unlabelled random graphs, J. Graph Theory 15 (1991), 303–316.

[31] T., Łuczak, L., Pyber, On random generation of the symmetric group, Combinatorics, Probability & Computing 2 (1993), 505–512.Google Scholar

[32] R., Meshulam, N., Wallach, Homological connectivity of random kdimensional complexes, Random Structures & Algorithms 34 (2009), 408–417.Google Scholar

[33] T., OdrzygóźdźThe square model for random groups, arXiv:1405.2773.

[34] Y., Ollivier, A January 2005 invitation to random groups, Ensaios Matematicos [Mathematical Surveys] 10, Sociedade Brasileira de Matematica, Rio de Janeiro, 2005.

[35] Y., Ollivier, Random group update, http://www.yannollivier.org/rech/publs/rgupdates.pdf.

[36] Y., Ollivier, D. T., Wise, Cubulating random groups at density less than 1/6, Trans. Amer. Math. Soc. 363 (2011), no. 9, 4701–4733.

[37] T., Tao, The dichotomy between structure and randomness, arithmetic progressions, and the primes, International Congress of Mathematicians. Vol. I, 581–608, Eur. Math. Soc., Zürich, 2007.Google Scholar

[38] A., Żuk, Property (T) and Kazhdan constants for discrete groups, Geom. Funct. Anal. 13 (2003), 643–670.Google Scholar