An analysis of one-dimensional Schelling segregation

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn , Issue , 2012, Pages 789-803

  Brandt, Christina ^a   Immorlica, Nicole ^b   Kamath, Gautam ^c   Kleinberg, Robert ^c  

^a Stanford University   (United States)

^b Northwestern University   (United States)

^c Department of Computer Science and School of Operations Research and Information Engineering   (United States)

Author keywords

agent based models; schelling segregation; stochastic processes in graphs

Indexed keywords

AGENT-BASED MODEL; APPROXIMATE ANALYSIS; AVERAGE SIZE; FINAL STATE; NEAREST NEIGHBORS; RIGOROUS ANALYSIS; SCHELLING; STABLE STATE;

DYNAMICS; RANDOM PROCESSES;

COMPUTATION THEORY;

EID: 84862611809     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/2213977.2214048     Document Type: Conference Paper

References (57)

1. D. Achlioptas. Lower bounds for random 3-sat via differential equations. Theoretical Computer Science, 265(1-2):159-185, 2001. (Pubitemid 32775941)
2. D. Achlioptas, R. M. D'Souza, and J. Spencer. Explosive percolation in random networks. Science, 323:1453-1455, 2009.
3. R. Alba and J. Logan. Minority proximity to whites in suburbs: An individual-level analysis of segregation. American Journal of Sociology, pages 1388-1427, 1993. (Pubitemid 24386024)
4. D. Aldous. Emergence of the giant component in special Marcus-Lushnikov processes. Random Structures and Algorithms, 12:179-196, 1998.
5. D. André. Solution directe du problème résolu par M. Bertrand. Comptes Rendus de l'Académie des Sciences, Paris, 105:436-437, 1887.
6. S. Bardea. Back to the future: A simple solution to Schelling segregation. Documents de Travail de l'OFCE, 2011.
7. S. Benard and R. Willer. A wealth and status-based model of residential segregation. The Journal of Mathematical Sociology, 31:149-174, Mar. 2007.
8. I. Benenson, E. Hatna, and E. Or. From Schelling to spatially explicit modeling of urban ethnic and economic residential dynamics. Sociological Methods & Research, 37(4):463, 2009.
9. J. Bertrand. Solution d'un problème. Comptes Rendus de l'Académie des Sciences, Paris, 105:369, 1887.
10. L. Blume. The statistical mechanics of strategic interaction. Games and Economic Behavior, 5(3):387-424, 1993.
11. L. Blume. The statistical mechanics of best-response strategy revision. Games and Economic Behavior, 11(2):111-145, 1995.
12. T. Bohman and A. Frieze. Avoiding a giant component. Random Structures and Algorithms, 19:75-85, 2001.
13. M. Bovens and M. Trappenburg. Segregation through anti-discrimination: How the netherlands got divided again. In M. Verweij and M. Thompson, editors, Clumsy Solutions for a Complex World. Palgrave MacMillan, 2006.
14. F. Brauer and J. A. Nohel. The Qualitative Theory of Ordinary Differential Equations. Dover, 1989.
15. M. T. Chao and J. Franco. Probabilistic analysis of two heuristics for the 3-satisfiability problem. SIAM J. Computing, 15:1106-1118, 1986. (Pubitemid 17465858)
16. W. Clark. Residential segregation in American cities: A review and interpretation. Population Research and Policy Review, 5(2):95-127, 1986.
17. W. Clark. Geography, space, and science: Perspectives from studies of migration and geographical sorting. Geographical Analysis, 40(3):258-275, 2008.
18. W. Clark and M. Fossett. Understanding the social context of the Schelling segregation model. Proceedings of the National Academy of Sciences, 105(11):4109, 2008.
19. D. Coppersmith, D. Gamarnik, M. T. Hajiaghayi, and G. Sorkin. Random MAX 2-SAT and MAX CUT. Random Structures and Algorithms, 24(4):502-545, 2004.
20. L. Dall'Asta, C. Castellano, and M. Marsili. Statistical physics of the Schelling model of segregation. Journal of Statistical Mechanics: Theory and Experiment, 2008:L07002, 2008.
21. E. Don-Yehiya. Religion and political accommodation in Israel. Jerusalem: Floersheimer Institute for Policy Studies, 1999.
22. A. Dvoretzky and T. Motzkin. A problem of arrangements. Duke Math J., 14:305-313, 1947.
23. G. Ellison. Learning, local interaction, and coordination. Econometrica, 61:1047-1072, 1993.
24. M. Emerson, K. Chai, and G. Yancey. Does race matter in residential segregation? Exploring the preferences of white americans. American Sociological Review, pages 922-935, 2001. (Pubitemid 34096520)
25. R. Farley, C. Steeh, T. Jackson, M. Krysan, and K. Reeves. Continued racial residential segregation in Detroit: "Chocolate city, vanilla suburbs" revisited. Journal of Housing Research, 4(1):1-38, 1993.
26. W. Feller. An Introduction to Probability Theory and Its Applications, volume 1. Wiley, 1968.
27. A. D. Flaxman, D. Gamarnik, and G. B. Sorkin. Embracing the giant component. Random Structures and Algorithms, 27:277-289, 2005. (Pubitemid 41640433)
28. D. Foster and H. P. Young. Stochastic evolutionary game dynamics. Theoretical Population Biology, 38:219-232, 1990.
29. A. Frieze and S. Suen. Analysis of two simple heuristics on a random instance of k-SAT. J. Algorithms, 20:312-355, 1996. (Pubitemid 126412188)
30. S. Gerhold, L. Glebsky, C. Schneider, H. Weiss, and B. Zimmermann. Limit states for one-dimensional Schelling segregation models. Communications in Nonlinear Science and Numerical Simulation, 13(10):2236-2245, 2008.
31. M. X. Goemans, V. S. Mirrokni, and A. Vetta. Sink equilibria and convergence. In Proc. 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS), pages 142-154, 2005.
32. S. Grauwin, F. Goffette-Nagot, and P. Jensen. Dynamic models of residential segregation: Brief review, analytical resolution and study of the introduction of coordination. Arxiv preprint arXiv:0907.1777, 2009.
33. A. D. Henry, P. Pralat, and C. Zhang. Emergence of segregation in evolving social networks. Proceedings of the National Academy of Sciences, 108(21):8605-8610, May 2011.
34. M. Kandori, G. Mailith, and R. Rob. Learning, mutation, and long run equilibria in games. Econometrica, 61:29-56, 1993.
35. R. M. Karp and M. Sipser. Maximum matchings in sparse random graphs. In Proceedings of the Twenty-Second Annual IEEE Symposium on Foundations of Computing (FOCS), pages 364-375, 1981.
36. W. v. d. Laan Bouma-Doff. Involuntary isolation: Ethnic preferences and residential segregation. Journal of urban affairs, 29(3):289-309, 2007.
37. D. Lambiri and M. Vargas. Residential segregation and public housing policy, the case of chile. Working Papers 29, Facultad de Economía y Empresa, Universidad Diego Portales, Aug. 2011.
38. D. S. Massey, A. B. Gross, and K. Shibuya. Migration, segregation, and the geographic concentration of poverty. American Sociological Review, 59(3):425-445, June 1994.
39. R. McCrea. Explaining sociospatial patterns in South East Queensland, Australia: Social homophily versus structural homophily. Environment and Planning A, 41(9):2201-2214, 2009.
40. M. Molloy and B. Reed. The size of the giant component of a random graph with a given degree sequence. Combinatorics, Probability and Computing, 7:295-305, 1998. (Pubitemid 128480814)
41. A. Montanari and A. Saberi. Convergence to equilibrium in local interaction games. In Proc. 50th Annual IEEE Symposium on Foundations of Computer Science (FOCS), pages 303-312, 2009.
42. R. Pancs and N. Vriend. Schelling's spatial proximity model of segregation revisited. Journal of Public Economics, 91(1-2):1-24, 2007. (Pubitemid 44856505)
43. M. Renault. Four proofs of the ballot theorem. Mathematics Magazine, 80(5):345-352, 2007.
44. O. Riordan and L. Warnke. Explosive percolation is continuous. Science, 333:322-324, 2011.
45. T. Schelling. Models of segregation. The American Economic Review, pages 488-493, 1969.
46. T. Schelling. Dynamic models of segregation. Journal of Mathematical Sociology, 1(2):143-186, 1971.
47. T. Schelling. The strategy of conflict. Harvard Univ Pr, 1980.
48. A. Singh, D. Vainchtein, and H. Weiss. Schelling's segregation model: Parameters, scaling, and aggregation. Arxiv preprint arXiv:0711.2212, 2007.
49. J. Spencer and N. Wormald. Birth control for giants. Combinatorica, 27:587-628, 2007.
50. M. White. Segregation and diversity measures in population distribution. Population index, 52(2):198-221, 1986.
51. N. C. Wormald. Differential equations for random processes and random graphs. Annals of Applied Probability, 5:1217-1235, 1995.
52. N. C. Wormald. The differential equation method for random graph processes and greedy algorithms. In M. Karoński and H. J. Prömel, editors, Lectures on Approximation and Randomized Algorithms, pages 73-155. PWN, 1999.
53. H. P. Young. The evolution of conventions. Econometrica, 61:57-84, 1993.
54. H. P. Young. Individual strategy and social structure: an evolutionary theory of institutions. Princeton University Press, Jan. 2001.
55. J. Zhang. A dynamic model of residential segregation. Journal of Mathematical Sociology, 28(3):147-170, 2004. (Pubitemid 39289007)
56. J. Zhang. Residential segregation in an all-integrationist world. Journal of Economic Behavior & Organization, 54(4):533-550, 2004. (Pubitemid 38990030)
57. J. Zhang. Tipping and residential segregation: A unified Schelling model. Journal of Regional Science, 51:167-193, Feb. 2011.