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Personal profile

Research interests

My research is mainly in pure and applied probability; I am a member of the ProbL@B (Probability Laboratory at Bath).

I work in a number of interconnected areas, mostly in and around Stochastic Geometry. My recent and current areas of research activity include the following: discrete and continuous percolation; interacting particle systems, particularly models of spatial deposition, and the resulting point processes; random packing of hard spheres; limit theorems in stochastic geometry, including rates of convergence and applications; spatial random networks, for example random geometric graphs and also directed and dynamical random networks; stochastic combinatorics, e.g. allocation models and random matrices; stochastic analysis on Poisson spaces - Stein's method and Malliavin calculus.

My monograph 'Random Geometric Graphs' (Oxford University Press, 2003) continues to inform some (though not all) of my research (and that of others).

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Poisson process Mathematics
Random Geometric Graph Mathematics
Stochastic Geometry Mathematics
Point Process Mathematics
Random Sequential Adsorption Mathematics
Boolean Model Mathematics
Central limit theorem Mathematics
Adsorption Engineering & Materials Science

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Projects 2010 2011

Research Output 2001 2019

Optimal Cheeger cuts and bisections of random geometric graphs

Penrose, M. & Müller, T., 14 Sep 2019, (Accepted/In press) In : Annals of Applied Probability. 33 p.

Research output: Contribution to journalArticle

Open Access
1 Citation (Scopus)
20 Downloads (Pure)

Inhomogeneous random graphs, isolated vertices, and Poisson approximation

Penrose, M. D., 1 Mar 2018, In : Journal of Applied Probability. 55, 1, p. 112-136 25 p.

Research output: Contribution to journalArticle

Open Access
Poisson Approximation
Random Graphs
Stein's Method
Poisson Point Process
1 Citation (Scopus)

Non-triviality of the vacancy phase transition for the Boolean model

Penrose, M., 31 Jul 2018, In : Electronic Communications in Probability. 23, 49, p. 1-8 8 p., 49.

Research output: Contribution to journalArticle

Open Access
Boolean Model
Poisson Model
Strictly positive
22 Downloads (Pure)

On the critical threshold for continuum AB percolation

Dereudre, D. & Penrose, M., 1 Dec 2018, In : Journal of Applied Probability. p. 1228-1237

Research output: Contribution to journalArticle

Open Access

Lectures on the Poisson Process

Last, G. & Penrose, M., 21 Dec 2017, Cambridge University Press. 313 p.

Research output: Book/ReportBook

Stochastic Geometry
Poisson process
Boolean Model
Stochastic Analysis
Measure space


Critical values in continuum and dependent percolation

Author: Rosoman, T., 1 Jun 2011

Supervisor: Penrose, M. (Supervisor)

Student thesis: Doctoral ThesisPhD


On the phase transition in certain percolation models.

Author: Daniels, C., 22 Feb 2016

Supervisor: Penrose, M. (Supervisor) & Matthies, K. (Supervisor)

Student thesis: Doctoral ThesisPhD