Random Geometric Graphs

By C. Cannings. 2005

821 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/508b01706129a6b36b8d545f2d0fa0fc6c4dda8e

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In Signal Processing

Citations in the corpus

Base-Station Assisted Device-to-Device Communications for High-Throughput Wireless Video Networks (2013, background): “ﬁed description of the physical layer, namely the protocol model, widely used in networking: two users can communicate if their physical distance 8 is smaller than some collaboration distance r [11], [16]. The maximum allowable distance for D2D communication ris determined by the power level for eac”
Persistent homology for random fields and complexes (2010, background): “racteristic is approximately 0 (for the last time and so implying coverage) when nis around (1=˝)log(1=˝) plus lower order terms. See [21] for more details. Interestingly, it follows from the work of [33] that the phase transition for the giant component to form, in the sense of random graph theory,”
Random geometric complexes in the thermodynamic regime (2014, background): “[1, 30]), and so this case will appear only peripherally in what follows.”
Lectures on the Poisson Process (2017, background): “We also extend our remit to topics in stochastic geometry, which is concerned with mathematical models for random geometric structures [4, 5, 23, 45, 123, 126, 147].”
Limit theorems for network dependent random variables (2019, methodology): “For example, these conditions are satisfied under the condition that the Berry-Esseen bound for normal approximation in Theorem 2.3 of Penrose (2003) converges to zero.”
Probability measures on the space of persistence diagrams (2011, background): “Most of the related work on stochastic aspects of topological summaries can be subdivided into two categories: the study of random abstract simplicial complexes generated from stochastic processes [5, 6, 7, 8, 9] and convergence or consistency of topological summaries as the number of points goes to”
Sampling-based algorithms for optimal motion planning (2011, background): “The function p∞ : λ → p∞( λ) is monotone, and p∞( 0)= 0 and limλ→∞ p∞( λ)= 1 (Penrose 2003).”
Estimation of geodesic tortuosity and constrictivity in stationary random closed sets (2018, methodology): “In the setting of tubes with periodically appearing bottlenecks, constrictivity is intimately related to the concept of effective diffusivity (Petersen, 1958). More recently, the definition of constrictivity was extended to complex microstructures based on the continuous pore size distribution (Holz”
Limit theorems for Betti numbers of random simplicial complexes (2010, result): “The proof is identical to that of the analogous result in Chapter 3 of Penrose [3].”
Gossip consensus algorithms via quantized communication (2009, methodology): “We have depicted the value of z for a family of random geometric graphs [15] of increasing size from N = 10 up to N = 80.”
High-dimensional random geometric graphs and their clique number (2011, methodology): “We refer to Penrose [16] for an extensive treatment.”