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Volumn 147, Issue 1, 2010, Pages 123-159

A phase transition behavior for Brownian motions interacting through their ranks

Author keywords

Atlas model; Interacting diffusions; McKean Vlasov; Phase transition; Poisson Dirichlet; Rank dependent processes

Indexed keywords


EID: 76949097014     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00440-009-0203-0     Document Type: Article
Times cited : (43)

References (38)
  • 1
    • 37449010568 scopus 로고
    • Abramowitz, M., Stegun, I. (eds.): Pocketbook of mathematical functions, Material selected by Michael Danos and Johann Rafelski. Verlag Harri Deutsch, Thun
    • Abramowitz, M., Stegun, I. (eds.): Pocketbook of mathematical functions. Abridged edition of Handbook of mathematical functions. Material selected by Michael Danos and Johann Rafelski. Verlag Harri Deutsch, Thun (1984).
    • (1984) Abridged edition of Handbook of mathematical functions
  • 3
    • 35548972560 scopus 로고    scopus 로고
    • A dynamical characterization of Poisson-Dirichlet distributions
    • Arguin L-P.: A dynamical characterization of Poisson-Dirichlet distributions. Electron. Commun. Probab. 12, 283-290 (2007).
    • (2007) Electron. Commun. Probab. , vol.12 , pp. 283-290
    • Arguin, L.-P.1
  • 4
    • 0000554761 scopus 로고
    • The motion of a tagged particle in the simple symmetric exclusion system on Z
    • Arratia R.: The motion of a tagged particle in the simple symmetric exclusion system on Z. Ann. Probab. 11(2), 362-373 (1983).
    • (1983) Ann. Probab. , vol.11 , Issue.2 , pp. 362-373
    • Arratia, R.1
  • 5
    • 0002241483 scopus 로고
    • Symmetric exclusion processes: A comparison inequality and a large deviation result
    • Arratia R.: Symmetric exclusion processes: a comparison inequality and a large deviation result. Ann. Probab. 13(1), 53-61 (1985).
    • (1985) Ann. Probab. , vol.13 , Issue.1 , pp. 53-61
    • Arratia, R.1
  • 8
    • 0033233673 scopus 로고    scopus 로고
    • Isoperimetric and analytic inequalities for log-concave probability measures
    • Bobkov S. G.: Isoperimetric and analytic inequalities for log-concave probability measures. Ann. Probab. 27(4), 1903-1921 (1999).
    • (1999) Ann. Probab. , vol.27 , Issue.4 , pp. 1903-1921
    • Bobkov, S.G.1
  • 9
    • 33845889473 scopus 로고    scopus 로고
    • Quantitative concentration inequalities for empirical measures on non-compact spaces
    • (To appear)
    • Bolley, F., Guillin, A., Villani, C.: Quantitative concentration inequalities for empirical measures on non-compact spaces. Probab. Theory Relat. Fields (To appear) (2007).
    • (2007) Probab. Theory Relat. Fields
    • Bolley, F.1    Guillin, A.2    Villani, C.3
  • 10
    • 0031539944 scopus 로고    scopus 로고
    • A stochastic particle method for the Mckean-Vlasov and the Burgers equation
    • Bossy M., Talay D.: A stochastic particle method for the Mckean-Vlasov and the Burgers equation. Math. Comput. 66(217), 157-192 (1997).
    • (1997) Math. Comput. , vol.66 , Issue.217 , pp. 157-192
    • Bossy, M.1    Talay, D.2
  • 12
    • 76949087336 scopus 로고    scopus 로고
    • Probabilistic approach for granular media equations in the non uniformly convex case
    • (to appear)
    • Cattiaux, P., Guillin, A., and Malrieu, F.: Probabilistic approach for granular media equations in the non uniformly convex case. Probab. Theory Relat. Fields (2007) (to appear).
    • (2007) Probab. Theory Relat. Fields
    • Cattiaux, P.1    Guillin, A.2    Malrieu, F.3
  • 15
    • 0001008463 scopus 로고
    • Diffusion with "collisions" between particles
    • Harris T. E.: Diffusion with "collisions" between particles. J. Appl. Probab. 2, 323-338 (1965).
    • (1965) J. Appl. Probab. , vol.2 , pp. 323-338
    • Harris, T.E.1
  • 16
    • 0040818321 scopus 로고
    • The heavy traffic approximation for single server queues in series
    • Harrison J. M.: The heavy traffic approximation for single server queues in series. J. Appl. Probab. 10, 613-629 (1973).
    • (1973) J. Appl. Probab. , vol.10 , pp. 613-629
    • Harrison, J.M.1
  • 17
    • 0034344279 scopus 로고    scopus 로고
    • Brownian models of open processing networks: Canonical representation of workload
    • Harrison J. M.: Brownian models of open processing networks: canonical representation of workload. Ann. Appl. Probab. 10(1), 75-103 (2000).
    • (2000) Ann. Appl. Probab. , vol.10 , Issue.1 , pp. 75-103
    • Harrison, J.M.1
  • 18
    • 0031484861 scopus 로고    scopus 로고
    • Dynamic control of Brownian networks: State space collapse and equivalent workload formulations
    • Harrison J. M., van Mieghem J. A.: Dynamic control of Brownian networks: state space collapse and equivalent workload formulations. Ann. Appl. Probab. 7(3), 747-771 (1997).
    • (1997) Ann. Appl. Probab. , vol.7 , Issue.3 , pp. 747-771
    • Harrison, J.M.1    van mieghem, J.A.2
  • 19
    • 0002500631 scopus 로고
    • Brownian models of open queueing networks with homogeneous customer populations
    • Harrison J. M., Williams R. J.: Brownian models of open queueing networks with homogeneous customer populations. Stochastics 22(2), 77-115 (1987).
    • (1987) Stochastics , vol.22 , Issue.2 , pp. 77-115
    • Harrison, J.M.1    Williams, R.J.2
  • 20
    • 0000427740 scopus 로고
    • The diffusion approximation for tandem queues in heavy traffic
    • Harrison J. M.: The diffusion approximation for tandem queues in heavy traffic. Adv. Appl. Probab. 10(4), 886-905 (1978).
    • (1978) Adv. Appl. Probab. , vol.10 , Issue.4 , pp. 886-905
    • Harrison, J.M.1
  • 21
    • 0034348036 scopus 로고    scopus 로고
    • An evolutionary model of the size distribution of firms
    • Hashemi F.: An evolutionary model of the size distribution of firms. J. Evol. Econ. 10, 507-521 (2000).
    • (2000) J. Evol. Econ. , vol.10 , pp. 507-521
    • Hashemi, F.1
  • 23
    • 0001525144 scopus 로고
    • Interpretations of departures from the Pareto curve firm-size distributions
    • Ijiri Y., Simon H.: Interpretations of departures from the Pareto curve firm-size distributions. J. Polit. Econ. 82, 315-331 (1977).
    • (1977) J. Polit. Econ. , vol.82 , pp. 315-331
    • Ijiri, Y.1    Simon, H.2
  • 24
    • 0003352140 scopus 로고    scopus 로고
    • Diffusion processes associated with nonlinear evolution equations for signed measures
    • Jourdain B.: Diffusion processes associated with nonlinear evolution equations for signed measures. Methodol. Comput. Appl. Probab. 2(1), 69-91 (2000).
    • (2000) Methodol. Comput. Appl. Probab. , vol.2 , Issue.1 , pp. 69-91
    • Jourdain, B.1
  • 25
    • 63049126592 scopus 로고    scopus 로고
    • Propagation of chaos and Poincaré inequalities for a system of particles interacting through their cdf
    • Jourdain B., Malrieu F.: Propagation of chaos and Poincaré inequalities for a system of particles interacting through their cdf. Ann. Appl. Probab. 18(5), 1706-1736 (2008).
    • (2008) Ann. Appl. Probab. , vol.18 , Issue.5 , pp. 1706-1736
    • Jourdain, B.1    Malrieu, F.2
  • 26
    • 0002485234 scopus 로고
    • Selection and the evolution of industry
    • Jovanovic B.: Selection and the evolution of industry. Econometrica 50, 649-670 (1982).
    • (1982) Econometrica , vol.50 , pp. 649-670
    • Jovanovic, B.1
  • 27
    • 0042408385 scopus 로고    scopus 로고
    • Logarithmic Sobolev inequalities for some nonlinear PDE's
    • Malrieu F.: Logarithmic Sobolev inequalities for some nonlinear PDE's. Stoch. Process. Appl. 95(1), 109-132 (2001).
    • (2001) Stoch. Process. Appl. , vol.95 , Issue.1 , pp. 109-132
    • Malrieu, F.1
  • 29
    • 0031534984 scopus 로고    scopus 로고
    • The two parameter Poisson-Dirichlet distribution derived from a stable subordinator
    • Pitman J., Yor M.: The two parameter Poisson-Dirichlet distribution derived from a stable subordinator. Ann. Probab. 25(2), 855-900 (1997).
    • (1997) Ann. Probab. , vol.25 , Issue.2 , pp. 855-900
    • Pitman, J.1    Yor, M.2
  • 32
    • 14944383950 scopus 로고    scopus 로고
    • Characterization of invariant measures at the leading edge for competing particle systems
    • Ruzmaikina A., Aizenman M.: Characterization of invariant measures at the leading edge for competing particle systems. Ann. Probab. 33(1), 82-113 (2005).
    • (2005) Ann. Probab. , vol.33 , Issue.1 , pp. 82-113
    • Ruzmaikina, A.1    Aizenman, M.2
  • 33
    • 0001129032 scopus 로고
    • The size distribution of business firms
    • Simon H., Bonini C.: The size distribution of business firms. Am. Econ. Rev. 48, 607-617 (1955).
    • (1955) Am. Econ. Rev. , vol.48 , pp. 607-617
    • Simon, H.1    Bonini, C.2
  • 34
    • 0038173084 scopus 로고
    • A propagation of chaos result for Burgers' equation
    • Sznitman A. S.: A propagation of chaos result for Burgers' equation. Probab. Theory Relat. Fields 71(4), 581-613 (1986).
    • (1986) Probab. Theory Relat. Fields , vol.71 , Issue.4 , pp. 581-613
    • Sznitman, A.S.1
  • 36
    • 0004313816 scopus 로고    scopus 로고
    • Spin Glasses: A Challenge for Mathematicians: Cavity and Mean Field Models
    • 1st edn.Springer, Heidelberg
    • Talagrand, M.: Spin Glasses: A Challenge for Mathematicians: Cavity and Mean Field Models, 1st edn. A Series of Modern Surveys in Mathematics. Springer, Heidelberg (2003).
    • (2003) A Series of Modern Surveys in Mathematics
    • Talagrand, M.1
  • 37
    • 84990581872 scopus 로고
    • Brownian motion in a wedge with oblique reflection
    • Varadhan S. R. S., Williams R. J.: Brownian motion in a wedge with oblique reflection. Comm. Pure Appl. Math. 38, 405-443 (1985).
    • (1985) Comm. Pure Appl. Math. , vol.38 , pp. 405-443
    • Varadhan, S.R.S.1    Williams, R.J.2
  • 38
    • 0001536669 scopus 로고
    • Reflected Brownian motion with skew symmetric data in a polyhedral domain
    • Williams R. J.: Reflected Brownian motion with skew symmetric data in a polyhedral domain. Probab. Theory Relat. Fields 75(4), 459-485 (1987).
    • (1987) Probab. Theory Relat. Fields , vol.75 , Issue.4 , pp. 459-485
    • Williams, R.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.