D. Aldous and J. M. Steele, The Objective Method: Probabilistic Combinatorial Optimization and Local Weak Convergence, pp.1-72, 2004.
DOI : 10.1007/978-3-662-09444-0_1

K. S. Alexander, Percolation and Minimal Spanning Forests in Infinite Graphs, The Annals of Probability, vol.23, issue.1, pp.87-104, 1995.
DOI : 10.1214/aop/1176988378

K. B. Athreya and P. Ney, A new approach to the limit theory of recurrent Markov chains, Transactions of the American Mathematical Society, vol.245, pp.493-501, 1978.
DOI : 10.1090/S0002-9947-1978-0511425-0

A. G. Bhatt and R. Roy, On a random directed spanning tree Advances in Applied Probabilty, pp.19-42, 2004.

D. J. Daley, D. Vere, and -. , An introduction to the Theory of Point Processes, 1988.

W. Feller, An Introduction to Probability Theory and its Applications, II. Wiley Series in Probability and Mathematical Statistics, 1971.

P. A. Ferrari, L. R. Fontes, and X. Wu, Twodimensional poisson trees converge to the brownian web, 2003.

P. A. Ferrari, C. Landim, and H. Thorisson, Poisson trees, succession lines and coalescing random walks, 2003.

L. R. Fontes, M. Isopi, C. M. Newman, and K. Ravishankar, The Brownian web: Characterization and convergence, The Annals of Probability, vol.32, issue.4, pp.2857-2883, 2004.
DOI : 10.1214/009117904000000568

S. Gangopadhyay, R. Roy, and A. Sarkar, Random oriented trees : a model of drainage networks, Annals in Applied Probability, vol.14, pp.1242-1266, 2004.

A. Gut, Convergence Rates for Probabilities of Moderate Deviations for Sums of Random Variables with Multidimensional Indices, The Annals of Probability, vol.8, issue.2, pp.298-313, 1980.
DOI : 10.1214/aop/1176994778

C. Howard and C. Newman, Geodesics and spanning trees for euclidean first-passage percolation, Ann. Probab, vol.29, pp.577-623, 2001.

S. Lee, The central limit theorem for euclidian minimal spanning trees, The Annals of Applied Probability, vol.7, pp.996-1020, 1997.
DOI : 10.1017/s0001867800009551

S. Meyn and R. Tweedie, Markov Chains and Stochastic Stability, 1993.

M. Penrose, Random Geometric Graphs. Oxford Studies in Probability, 2003.

M. Penrose and A. Wade, On the total length of the random minimal directed spanning tree. preprint math.PR/0409201 from arxiv.org, 2004.

M. Penrose and A. Wade, Random minimal directed spanning trees and Dickman-type distributions, Advances in Applied Probability, vol.1, issue.03, pp.691-714, 2004.
DOI : 10.1007/PL00009241

M. Penrose and J. Yukich, Limit Theory for Random Sequential Packing and Deposition, The Annals of Applied Probability, vol.12, issue.1, pp.272-301, 2001.
DOI : 10.1214/aoap/1015961164

M. Penrose and J. Yukich, Weak laws of large numbers in geometric probability, The Annals of Applied Probability, vol.13, issue.1, pp.277-303, 2003.
DOI : 10.1214/aoap/1042765669

W. Rhee, A Matching Problem and Subadditive Euclidean Functionals, The Annals of Applied Probability, vol.3, issue.3, pp.794-801, 1993.
DOI : 10.1214/aoap/1177005364

J. M. Steele, Probability Theory and Combinatorial Optimization. NSF- CBMS, 1997.

M. Talagrand, Concentration of measure and isoperimetric inequalities in product spaces. Publications Mathematiques de l'I, pp.73-205, 1995.

B. Toth and W. Werner, The true self repelling motion. Probability Theory and Related Fields, pp.375-452, 1998.

J. Yukich, Probability Theory of Classical Euclidean Optimization Problems, Lecture Notes in Mathematics, vol.1675, 1998.
DOI : 10.1007/BFb0093472

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