A stable marriage of poisson and lebesgue

Annals of Probability

Volumn 34, Issue 4, 2006, Pages 1241-1272

  Hoffman, Christopher ^a   Holroyd, Alexander E ^b   Peres, Yuval ^c  

^a UNIVERSITY OF WASHINGTON   (United States)

^b UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Phase transition; Point process; Stable marriage

Indexed keywords

EID: 33750177601     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/009117906000000098     Document Type: Article

References (17)

1. ALDOUS, D. J. (2000). The percolation process on a tree where infinite clusters are frozen. Math. Proc. Cambridge Philos. Soc. 128 465-477. MR1744108
2. BENJAMINI, I., LYONS, R., PERES, Y. and SCHRAMM, O. (1999). Group-invariant percolation on graphs. Geom. Funct. Anal. 9 29-66. MR1675890
3. CARLESON, L. (1967). Selected Problems on Exceptional Sets. Van Nostrand, Princeton, NJ. MR0225986
4. DOYLE, P. G. and SNELL, J. L. (1984). Random Walks and Electric Networks. Mathematical Association of America, Washington, DC. MR0920811
5. FREIRE, M. V., POPOV, S. and VACHKOVSKAIA, M. (2005). Percolation for the stable marriage of Poisson and Lebesgue. Preprint. math.PR/0511186.
6. GALE, D. and SHAPLEY, L. (1962). College admissions and stability of marriage. Amer. Math. Monthly 69 9-15. MR1531503
7. HÄGGSTRÖM, O. (1997). Infinite clusters in dependent automorphism invariant percolation on trees. Ann. Probab. 25 1423-1436. MR 1457624
8. HUFFMAN, C., HOLROYD, A. E. and PERES, Y. (2005). Tail bounds for the stable marriage of Poisson and Lebesgue. Preprint. math.PR/0507324.
9. HOLROYD, A. E. and LIGGETT, T. M. (2001). How to find an extra head: Optimal random shifts of Bernoulli and Poisson random fields. Ann. Probab. 29 1405-1425. MR1880225
10. HOLROYD, A. E. and PERES, Y. (2005). Extra heads and invariant allocations. Ann. Probab. 3331-52. MR2118858
11. KALLENBERG, O. (2002). Foundations of Modern Probability, 2nd ed. Springer, New York. MR1876169
12. KNUTH, D.E. (1997). Stable Marriage and Its Relation to Other Combinatorial Problems. Amer. Math. Soc., Providence, RI. MR1415126
13. LIGGETT, T. M. (2002). Tagged particle distributions or how to choose a head at random. In In and Out of Equilibrium 133-162. Birkhäuser, Boston. MR1901951
14. OKABE, A., BOOTS, B., SUGIHARA, K. and CHIU, S. N. (2000). Spatial Tessellations: Concepts and Applications of Voronoi diagrams, 2nd ed. Wiley, Chichester.
15. LYONS, R. and PERES, Y. (2006). Probability on Trees and Networks. Cambridge Univ. Press. Available at mypage.iu.edu/~rdlyons/prbtree/prbtree.html.
16. SOARDI, P. M. (1994). Potential Theory on Infinite Networks. Springer, Berlin. MR1324344
17. THORISSON, H. (1996). Transforming random elements and shifting random fields. Ann. Probab. 24 2057-2064. MR1415240