When does the top homology of a random simplicial complex vanish?
نویسندگان
چکیده
Several years ago Linial and Meshulam [8] introduced a model calledXd(n, p) of random n-vertex d-dimensional simplicial complexes. The following question suggests itself very naturally: What is the threshold probability p = p(n) at which the d-dimensional homology of such a random d-complex is, almost surely, nonzero? Here we derive an upper bound on this threshold. Computer experiments that we have conducted suggest that this bound may coincide with the actual threshold, but this remains an open question.
منابع مشابه
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 t...
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عنوان ژورنال:
- Random Struct. Algorithms
دوره 46 شماره
صفحات -
تاریخ انتشار 2015