Publications: Mathew D. Penrose

Book

Random Geometric Graphs (in preparation)

Refereed Papers

  1. `The minimum of a large number of Bessel processes', Journal of the London Math. Society 38, 566-576 (1989).
  2. `On the existence of self-intersections for quasi-every Brownian path in space,' Annals of Probability 17, 482-502 (1989). Possibly electronically available via JSTOR.
  3. `Quasi-everywhere properties of Brownian level sets and multiple points,' Stochastic Processes and their Applications 36 33-43 (1990).
  4. `Minima of independent Bessel processes and distances between Brownian particles', Journal of the London Math. Society 43, 355-366 (1991).
  5. `On a continuum percolation model', Advances in Applied Probability 23, 536-556 (1991). Abstract.
  6. `Semi-min-stable processes', Annals of Probability 20, 1450-1463 (1992). Possibly electronically available via JSTOR.
  7. `On path integrals for the high-dimensional Brownian bridge', with R. Pemantle, Journal of Compuational and Applied Mathematics 44, 381-390 (1992). Abstract.
  8. `On the spread-out limit for bond and continuum percolation', Annals of Applied Probability 3, 253-276 (1993). Electronic version from JSTOR.
  9. `Sticky spheres in quantum mechanics', with O.Penrose and G.Stell, Reviews in Mathematical Physics 6, 947-975 (1994). Also in The State of Matter, World Scientific (1994), pp. 106-141. Abstract.
  10. `Fluctuations of annihilations of Brownian spheres', Stochastic Processes and Applications 51, 167-189 (1994).
  11. `Self-avoiding walks and trees in spread-out lattices', Journal of Statistical Physics 77, 3-15 (1994). Abstract.
  12. `Generalized two-sample U-statistics and a two-species reaction-diffusion model'. Stochastic Processes and their Applications 55, 57-64 (1995). Abstract.
  13. `Single linkage clustering and continuum percolation'. Journal of Multivariate Analysis 53, 94-109 (1995). Abstract.
  14. `Large deviations for discrete and continuous percolation', with A. Pisztora, Advances in Applied Probability 28, 29-52 (1996). Abstract.
  15. `The threshold contact process: a continuum limit', Probability Theory and Related Fields 104, 77-96 (1996). Abstract.
  16. `Continuum percolation and Euclidean minimal spanning trees in high dimensions', Annals of Applied Probability 6, 528-544 (1996). Abstract. Possibly electronically available via JSTOR.
  17. `Spatial epidemics with large finite range'. Journal of Applied Probability 33, 933-939 (1996). Abstract.
  18. `The random minimal spanning tree in high dimensions'. Annals of Probability 24, 1903-1925 (1996). Abstract. Possibly electronically available via JSTOR.
  19. `The longest edge of the random minimal spanning tree', Annals of Applied Probability 7, 340-361 (1997). Abstract.
  20. `The random connection model in high dimensions', with R. Meester and A. Sarkar, Statistics and Probability Letters 35, 145-153 (1997). Abstract. Electronic connection via ScienceDirect.
  21. `Random minimal spanning tree and percolation on the N-cube'. Random Structures and Algorithms 12, 63-82 (1998). Abstract.
  22. `Extremes for the minimal spanning tree on normally distributed points', Advances in Applied Probability 30, 628-639 (1998) Abstract.
  23. `A strong law for the longest edge of the minimal spanning tree', Annals of Probability 27, 246-260 (1999) Abstract.
  24. `On the multivariate runs test', with N. Henze, Annals of Statistics 27, 290-298 (1999). Abstract.
  25. `On k-connectivity for a geometric random graph', Random Structures and Algorithms 15, 145-164 (1999). Abstract.
  26. `A strong law for the largest nearest-neighbour link between random points', Journal of the London Mathematical Society (2) 60,, 951-960 (1999). Abstract.
  27. `Poisson limits for pairwise and area interaction point processes', with S. Rao Jammalamadaka, Advances in Applied Probability 32, 75-85 (2000). Abstract.
  28. `Central limit theorems for k-nearest neighbour distances', Stochastic Processes and their Applications 85, 295-320 (2000). Abstract.
  29. `Vertex ordering and partitioning problems for random spatial graphs', Annals of Applied Probability 10, 517-538 (2000). Abstract.
  30. `Convergence theorems for some layout measures on random lattice and random geometric graphs', with J. Diaz, M. Serna, and J. Petit. Combinatorics, Probability and Computing 10 , 489-511 (2000).
  31. `A central limit theorem with applications to percolation, epidemics and Boolean models', Annals of Probability 29, 1515-1546 (2001). Abstract. ps file.
  32. `Random parking, sequential adsorption, and the jamming limit', Communications in Mathematical Physics 218 , 153-176 (2001). Abstract. ps file
  33. `Approximating layout problems on random graphs' with J. Diaz, M. Serna, and J. Petit. Journal of Algorithms 39, 78-117 (2001).
  34. `Limit theory for monolayer ballistic deposition in the continuum', Journal of Statistical Physics 105, 561-583 (2001). See cond-mat/0106163 at the e-print archive
  35. `Mathematics of random growing interfaces', with J.E. Yukich, Journal of Physics A: Math. Gen. 34, 6239-6247 (2001). Abstract. See Online version. Or see cond-mat/0106165 at the e-print archive
  36. `Central limit theorems for some graphs in computational geometry', with J.E. Yukich, Annals of Applied Probability 11, 1005-1041 (2001) Abstract.
  37. `Limit theorems for monotonic particle systems and sequential deposition', Stochastic Process and their Applications 98 175-197 (2002). Abstract. Electronic version from ScienceDirect.
  38. `Limit theory for random sequential packing and deposition', with J.E. Yukich, Annals of Applied Probability 12, 272-301 (2002). Abstract.

Other work

  1. `Some quasi-everywhere results on Wiener space'. Ph.D. Thesis, University of Ediinburgh, 1988.
  2. `The second virial coefficient for quantum-mechanical sticky spheres', with O. Penrose, in On three levels, ed. M. Fannes et al. Plenum press (1994) 381-384 Abstract.
  3. `Layout problems on lattice graphs', with J. Diaz, M. Serna, and J. Petit. Computing and Combinatorics: 5th Annual International Conference COCOON'99, Eds. T.Asano, H. Imai, D.T.Lee, S.Nakano and T.Tokuyzma, Springer (1999) 103-112.
  4. `Layout problems on lattice graphs', with J. Diaz, M. Serna, and J. Petit. Graph-Theoretic Concepts in Computer Science (WG'99) Eds. P. Widmayer, G. Neyer and S. Eidenbenz, Springer (1999) 291-302.
  5. `Lectures on particle systems and epidemics', in Percolation Theory and Particle Systems ed. R.Roy. Universities Press (India), Hyderabad (2000) 133-149. ps file
  6. `Weak laws in geometric probability', with J.E. Yukich, preprint (2001). Abstract. For text see math.PR/0107148 at the e-print archive
  7. `Focusing of the scan statistic and geometric clique number', preprint (2002). Abstract.

    Book Reviews

    1. R. Meester and R. Roy: Continuum Percolation, Bull. Amer. Math. Soc. 34, 447-448 (1997).
    2. R. Meester and R. Roy: Continuum Percolation. Bull. London Math. Soc. 30, 435-436 (1998).

    Last update 5 April 02