Random Geometric Complexes

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

Barishnokov, Y.: Quantum foam, August 2009. (Talk given at AIM Workshop on “Topological complexity of random sets”)

Björner, A.: Topological methods. In: Handbook of Combinatorics, vol. 2, pp. 1819–1872. Elsevier, Amsterdam (1995)

Bollobás, B., Riordan, O.: Clique percolation. Random Struct. Algorithms 35(3), 294–322 (2009)

Bubenik, P., Carlson, G., Kim, P.T., Luo, Z.M.: Statistical topology via Morse theory, persistence and nonparametric estimation. Algebr. Methods Stat. Probab. II 516, 75 (2010)

Bubenik, P., Kim, P.T.: A statistical approach to persistent homology. Homology Homotopy Appl. 9(2), 337–362 (2007)

Carlsson, G.: Topology and data. Bull. Am. Math. Soc. (N.S.) 46(2), 255–308 (2009)

Chambers, E.W., de Silva, V., Erickson, J., Ghrist, R.: Vietoris–Rips complexes of planar point sets. Discrete Comput. Geom. 44(1), 75–90 (2010)

Cohen-Steiner, D., Edelsbrunner, H., Harer, J.: Stability of persistence diagrams. Discrete Comput. Geom. 37(1), 103–120 (2007)

Diaconis, P.: Application of topology. Quicktime video, September 2006. (Talk given at MSRI Workshop on “Application of topology in science and engineering,” Quicktime video available on MSRI webpage)

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Gromov, M.: Random walk in random groups. Geom. Funct. Anal. 13(1), 73–146 (2003)

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Hausmann, J.-C.: On the Vietoris–Rips complexes and a cohomology theory for metric spaces. In: Prospects in Topology, Princeton, NJ, 1994. Ann. of Math. Stud., vol. 138, pp. 175–188. Princeton University Press, Princeton (1995)

Kahle, M.: The neighborhood complex of a random graph. J. Comb. Theory, Ser. A 114(2), 380–387 (2007)

Kahle, M.: Topology of random clique complexes. Discrete Math. 309(6), 1658–1671 (2009)

Kahle, M., Meckes, E.: Limit theorems for Betti numbers of random simplicial complexes. Submitted, arXiv:1009.4130 (2010)

Linial, N., Meshulam, R.: Homological connectivity of random 2-complexes. Combinatorica 26(4), 475–487 (2006)

Linial, N., Novik, I.: How neighborly can a centrally symmetric polytope be? Discrete Comput. Geom. 36(2), 273–281 (2006)

Meshulam, R., Wallach, N.: Homological connectivity of random k-dimensional complexes. Random Struct. Algorithms 34(3), 408–417 (2009)

Niyogi, P., Smale, S., Weinberger, S.: Finding the homology of submanifolds with high confidence from random samples. Discrete Comput. Geom. 39(1–3), 419–441 (2008)

Niyogi, P., Smale, S., Weinberger, S.: A topological view of unsupervised learning from noisy data (2010, to appear)

Penrose, M.: Random Geometric Graphs. Oxford Studies in Probability, vol. 5. Oxford University Press, Oxford (2003)

Pippenger, N., Schleich, K.: Topological characteristics of random triangulated surfaces. Random Struct. Algorithms 28(3), 247–288 (2006)

Vietoris, L.: Über den höheren Zusammenhang kompakter Räume und eine Klasse von zusammenhangstreuen Abbildungen. Math. Ann. 97(1), 454–472 (1927)

Zomorodian, A., Carlsson, G.: Computing persistent homology. Discrete Comput. Geom. 33(2), 249–274 (2005)