Random geometric complexes in the thermodynamic regime
نویسندگان
چکیده
منابع مشابه
Random Geometric Complexes
We study the expected topological properties of Čech and Vietoris-Rips complexes built on randomly sampled points in R. These are, in some cases, analogues of known results for connectivity and component counts for random geometric graphs. However, an important difference in this setting is that homology is not monotone in the underlying parameter. In the sparse range, we compute the expectatio...
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Let n be a positive integer, and λ > 0 a real number. Let Vn be a set of n points randomly located within the unit disk, which are mutually independent. For 1 ≤ p ≤ ∞, define Gp(λ, n) to be the graph with the vertex set Vn, in which two vertices are adjacent if and only if their `p-distance is at most λ. We call this graph a unit disk random graph. Let λ = c √ ln n/n and let X be the number of ...
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ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 2015
ISSN: 0178-8051,1432-2064
DOI: 10.1007/s00440-015-0678-9