random geometric complexes
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Author(s):  
Antonio Auffinger ◽  
Antonio Lerario ◽  
Erik Lundberg

Abstract We investigate the topologies of random geometric complexes built over random points sampled on Riemannian manifolds in the so-called “thermodynamic” regime. We prove the existence of universal limit laws for the topologies; namely, the random normalized counting measure of connected components (counted according to homotopy type) is shown to converge in probability to a deterministic probability measure. Moreover, we show that the support of the deterministic limiting measure equals the set of all homotopy types for Euclidean connected geometric complexes of the same dimension as the manifold.


2018 ◽  
Vol 1 (3-4) ◽  
pp. 331-364 ◽  
Author(s):  
Omer Bobrowski ◽  
Matthew Kahle

2017 ◽  
Vol 27 (4) ◽  
pp. 2032-2060 ◽  
Author(s):  
Omer Bobrowski ◽  
Matthew Kahle ◽  
Primoz Skraba

2015 ◽  
Vol 167 (1-2) ◽  
pp. 107-142 ◽  
Author(s):  
D. Yogeshwaran ◽  
Eliran Subag ◽  
Robert J. Adler

2011 ◽  
Vol 45 (3) ◽  
pp. 553-573 ◽  
Author(s):  
Matthew Kahle

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