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All issues Volume 20 (2016) ESAIM: PS, 20 (2016) 261-292 References
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Issue
ESAIM: PS
Volume 20, 2016
Page(s) 261 - 292
DOI https://doi.org/10.1051/ps/2016012
Published online 18 July 2016
  1. D.J. Aldous, Which connected spatial networks on random points have linear route-lengths? Preprint arXiv:0911.5296 (2009). [Google Scholar]
  2. F. Baccelli, K. Tchoumatchenko and S. Zuyev, Markov paths on the Poisson-Delaunay graph with applications to routeing in mobile networks. Adv. Appl. Probab. 32 (2000) 1–18. [CrossRef] [Google Scholar]
  3. F. Baccelli, D. Coupier and V. Tran, Semi-infinite paths of the 2D-radial spanning tree. Adv. Appl. Probab. 47 (2013) 814–844. [Google Scholar]
  4. M. Benaïm and R. Rossignol, Exponential concentration for first passage percolation through modified Poincaré inequalities. Ann. Inst. Henri Poincaré, Probab. Stat. 44 (2008) 544–573. [CrossRef] [MathSciNet] [Google Scholar]
  5. S. Boucheron, G. Lugosi and P. Massart, On concentration of self-bounding functions. Electron. J. Probab. 14 (2009) 1884–1899. [CrossRef] [MathSciNet] [Google Scholar]
  6. N. Chenavier and O. Devillers, Stretch factor of long paths in a planar Poisson−Delaunay triangulation. Preprint (2015). [Google Scholar]
  7. S.N. Chiu, D. Stoyan, W.S. Kendall and J. Mecke, Stochastic Geometry and its Applications. J. Wiley & Sons, Chichester, 3rd edition (2013). [Google Scholar]
  8. D. Coupier and V.C. Tran, The 2D-directed spanning forest is almost surely a tree. Random Structures & Algorithms 42 (2013) 59–72. [CrossRef] [MathSciNet] [Google Scholar]
  9. D.J. Daley and G. Last, Descending chains, the lilypond model, and mutual-nearest-neighbour matching. Adv. Appl. Probab. 37 (2005) 604–628. [CrossRef] [Google Scholar]
  10. O. Garet and R. Marchand, Moderate deviations for the chemical distance in Bernoulli percolation. Latin Amer. J. Probab. Math. Statist. 7 (2010) 171–191. [Google Scholar]
  11. C. Gloaguen, F. Voss and V. Schmidt, Parametric distributions of connection lengths for the efficient analysis of fixed access networks. Ann. Telecommun. 66 (2011) 103–118. [CrossRef] [Google Scholar]
  12. L. Heinrich and L. Muche, Second-order properties of the point process of nodes in a stationary Voronoi tessellation. Math. Nachr. 281 (2008) 350–375. [CrossRef] [MathSciNet] [Google Scholar]
  13. C. Hirsch, D. Neuhäuser, C. Gloaguen and V. Schmidt, Asymptotic properties of Euclidean shortest-path trees in random geometric graphs. Statist. Probab. Lett. 107 (2015) 122–130. [CrossRef] [MathSciNet] [Google Scholar]
  14. C. Hirsch, D. Neuhäuser, C. Gloaguen and V. Schmidt, First-passage percolation on random geometric graphs and an application to shortest-path trees. Adv. Appl. Probab. 47 (2015) 328–354. [CrossRef] [Google Scholar]
  15. C. Howard and C. Newman, Euclidean models of first-passage percolation. Probab. Theory Related Fields 108 (1997) 153–170. [CrossRef] [MathSciNet] [Google Scholar]
  16. C. Howard and C. Newman, Geodesics and spanning trees for Euclidean first-passage percolation. Ann. Probab. 29 (2001) 577–623. [Google Scholar]
  17. D. Illian, P. Penttinen, H. Stoyan and D. Stoyan, Statistical Analysis and Modelling of Spatial Point Patterns. J. Wiley & Sons, Chichester (2008). [Google Scholar]
  18. H. Kesten, On the speed of convergence in first-passage percolation. Ann. Appl. Probab. 3 (1993) 296–338. [CrossRef] [MathSciNet] [Google Scholar]
  19. C. Licea and C.M. Newman, Geodesics in two-dimensional first-passage percolation. Ann. Probab. 24 (1996) 399–410. [CrossRef] [MathSciNet] [Google Scholar]
  20. T.M. Liggett, R.H. Schonmann and A.M. Stacey, Domination by product measures. Ann. Probab. 25 (1997) 71–95. [CrossRef] [MathSciNet] [Google Scholar]
  21. C. McDiarmid, Concentration. In Probabilistic Methods for Algorithmic Discrete Mathematics. Edited by M. Habib, C. McDiarmid, J. Ramirez-Alfonsin and B. Reed. Springer, Berlin (1998) 195–248. [Google Scholar]
  22. D. Neuhäuser, C. Hirsch, C. Gloaguen and V. Schmidt, A parametric copula approach for modelling shortest-path trees in telecommunication networks. In Analytical and Stochastic Modeling Techniques and Applications, edited by A. Dudin and K. Turck. Vol. 7984 of Lect. Notes Comput. Sci. Springer, Berlin (2013) 324–336. [Google Scholar]
  23. C.M. Newman and M.S.T. Piza, Divergence of shape fluctuations in two dimensions. Ann. Probab. 23 (1995) 977–1005. [CrossRef] [MathSciNet] [Google Scholar]
  24. L. Pimentel, Multitype shape theorems for first-passage percolation models. Adv. Appl. Probab. 39 (2007) 53–76. [CrossRef] [MathSciNet] [Google Scholar]
  25. L. Pimentel, Asymptotics for first-passage times on Delaunay triangulations. Comb., Probab. Comput. 20 (2011) 435–453. [CrossRef] [Google Scholar]
  26. R. Schneider and W. Weil, Stochastic and Integral Geometry. Springer, Berlin (2008). [Google Scholar]
  27. M.Q. Vahidi-Asl and J.C. Wierman, First-passage percolation on the Voronoi tessellation and Delaunay triangulation. In Random Graphs’ 87, edited by M. Karoński, J. Jaworski and A. Ruciński. J. Wiley & Sons, Chichester (1990) 341–359. [Google Scholar]
  28. F. Voss, C. Gloaguen and V. Schmidt, Scaling limits for shortest path lengths along the edges of stationary tessellations. Adv. Appl. Probab. 42 (2010) 936–952. [CrossRef] [MathSciNet] [Google Scholar]

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