M
Mathew D. Penrose
Researcher at University of Bath
Publications - 136
Citations - 5214
Mathew D. Penrose is an academic researcher from University of Bath. The author has contributed to research in topics: Central limit theorem & Poisson distribution. The author has an hindex of 35, co-authored 133 publications receiving 4799 citations. Previous affiliations of Mathew D. Penrose include University of Edinburgh & University of California, Santa Barbara.
Papers
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The longest edge of the random minimal spanning tree
TL;DR: For n points placed uniformly at random on the unit square, it is known that the distribution of the minimal spanning tree on these points converges weakly to the double exponential as mentioned in this paper.
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On k-connectivity for a geometric random graph
TL;DR: For n points uniformly randomly distributed on the unit cube in d dimensions, with d≥2, let ρn (respectively, σn) denote the minimum r at which the graph, obtained by adding an edge between each pair of points distant at most r apart, is k-connected.
Book
Lectures on the Poisson Process
TL;DR: In this article, the authors developed the theory of the Poisson process in the setting of a general abstract measure space, establishing basic results and properties as well as certain advanced topics in the stochastic analysis of the poisson process.
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Central limit theorems for some graphs in computational geometry
TL;DR: In this article, a general central limit theorem for functionals of point sets was obtained by restricting a homogeneous Poisson process to the set of points in the set and then taking uniformly distributed points from the set.
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Weak laws of large numbers in geometric probability
TL;DR: In this article, a general weak law of large numbers for functionals of binomial point processes in d-dimensional space is established, with a limit that depends explicitly on the density of the point process.