MATH690 - Topics in Random Topology - Literature

[1] Robert J. Adler, Omer Bobrowski, and Shmuel Weinberger. Crackle: The Homology of Noise. Discrete & Computational Geometry, 52(4):680–704, December 2014. [2] Noga Alon. On the edge-expansion of graphs. Combinatorics, Probability and Computing, 6(02):145–152, 1997. [3] Noga Alon and Joel H. Spencer. The probabilistic method. John Wiley & Sons, 2004. [4] Lior Aronshtam and Nathan Linial. The threshold for d-collapsibility in random complexes*. Random Structures & Algorithms, 2015. [5] Lior Aronshtam and Nathan Linial. When does the top homology of a random simplicial complex vanish? Random Structures & Algorithms, 46(1):26–35, 2015. [6] Lior Aronshtam, Nathan Linial, Tomasz Luczak, and Roy Meshulam. Collapsibility and vanishing of top homology in random simplicial complexes. Discrete & Computational Geometry, 49(2):317–334, 2013. [7] Eric Babson. Fundamental groups of random clique complexes. arXiv preprint arXiv:1207.5028, 2012. [8] Eric Babson, Christopher Hoffman, and Matthew Kahle. The fundamental group of random 2-complexes. Journal of the American Mathematical Society, 24(1):1–28, 2011. [9] Itai Benjamini, Simi Haber, Michael Krivelevich, and Eyal Lubetzky. The isoperimetric constant of the random graph process. Random Structures & Algorithms, 32(1):101–114, 2008. [10] Omer Bobrowski and Robert J. Adler. Distance functions, critical points, and the topology of random čech complexes. Homology, Homotopy and Applications, 16(2):311–344, 2014. [11] Omer Bobrowski and Matthew Kahle. Topology of random geometric complexes: a survey. arXiv preprint arXiv:1409.4734, 2014. [12] Omer Bobrowski and Sayan Mukherjee. The topology of probability distributions on manifolds. Probability Theory and Related Fields, 161(3-4):651–686, 2014. [13] D. Cohen, Armindo Costa, Michael Farber, and Thomas Kappeler. Topology of random 2complexes. Discrete & Computational Geometry, 47(1):117–149, 2012. [14] Daniel C. Cohen, Michael Farber, and Thomas Kappeler. The homotopical dimension of random 2-complexes. arXiv preprint arXiv:1005.3383, 2010.