About the stationary states of vortex systems
Bodineau, Thierry ; Guionnet, Alice
Annales de l'I.H.P. Probabilités et statistiques, Tome 35 (1999), p. 205-237 / Harvested from Numdam
Publié le : 1999-01-01
@article{AIHPB_1999__35_2_205_0,
     author = {Bodineau, Thierry and Guionnet, Alice},
     title = {About the stationary states of vortex systems},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {35},
     year = {1999},
     pages = {205-237},
     mrnumber = {1678526},
     zbl = {0920.60095},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_1999__35_2_205_0}
}
Bodineau, Thierry; Guionnet, Alice. About the stationary states of vortex systems. Annales de l'I.H.P. Probabilités et statistiques, Tome 35 (1999) pp. 205-237. http://gdmltest.u-ga.fr/item/AIHPB_1999__35_2_205_0/

[1] M.A. Arcones, E. Gine, Limit Theorems for U-processes, Ann. Probab., Vol. 21, 1993, pp. 1494-1542. | MR 1235426 | Zbl 0789.60031

[2] G. Ben Arous, M. Brunaud, Méthode de Laplace : Etude variationnelle des fluctuations de diffusions de type "champ moyen", Stochastics , Vol. 31-32, 1990, pp. 79-144 | MR 1080535 | Zbl 0705.60046

[3] E. Caglioti, P.L. Lions, C. Marchioro, M. Pulvirenti, A special class of stationary flows for two dimensional Euler equations : A statistical mechanics description, Commun. Math. Phys., Vol. 143, 1991, pp. 501-525. | MR 1145596 | Zbl 0745.76001

[4] E. Caglioti, P.L. Lions, C. Marchioro, M. Pulvirenti, A special class of stationary flows for two dimensional Euler equations : A statistical mechanics description. Part 2 Commun. Math. Phys., Vol. 174, 1995, pp. 229-260. | MR 1362165 | Zbl 0840.76002

[5] A. Dembo, O. Zeitouni, Large deviations techniques and Applications. Jones and Bartlett, 1993. | MR 1202429 | Zbl 0793.60030

[6] J.-D. Deuschel, D.W. Stroock, Larges deviations, Academic Press, 1989. | MR 997938 | Zbl 0705.60029

[7] C. Deustch, M. Lavaud, Equilibrium properties of a two dimensional Coulomb gas, Phys. Rev. A, Vol. 9, 6, 1973, pp. 2598-2616.

[8] G.L. Eyink, H. Spohn, Negative-temperature states and large-scale, long-lived vortices in two-dimensional turbulence, J. Stat. Phys., Vol. 70, Nov. 3/4, 1993, pp. 833-886. | MR 1203717 | Zbl 0945.82568

[9] J. Fröhlich, Classical and quantum statistical mechanics in one and two dimensions, two component Yukawa and Coulomb systems, Commun. Math. Phys., Vol. 47, 1976, pp. 233-268. | MR 434278 | Zbl 01706170

[10] J. Fröhlich, D. Ruelle, Statistical mechanics of vortices in an inviscid two-dimensional fluid, Commun. Math. Phys., Vol. 87, 1982, pp. 1-36. | MR 680646 | Zbl 0505.76037

[11] A. Guionnet, Fluctuations for strongly interacting random variables and Wigner's law, to appear in Prob. Th. Rel. Fields, 1996.

[12] G. Joyce, D. Montgomery, Negative temperature states for the two dimensional guiding-centre plasma, J. Plasma Phys., Vol. 10, part 1, 1973, pp. 107-121.

[13] M. Kiessling, Statistical mechanics of classical particles with logarithmic interactions, Commun. Pure Appl. Math., Vol. 46, 1, 1993, pp. 27-56. | MR 1193342 | Zbl 0811.76002

[14] M. Kiessling, J. Lebowitz, The micro-canonical point vortex ensemble : beyond equivalence, Lett. Math. Phys., Vol. 42, 1, 1997, pp. 43-58. | MR 1473359 | Zbl 0902.76021

[15] C. Marchioro, M. Pulvirenti, Mathematical theory of incompressible nonviscous fluids, Springer, Applied Math. sciences, Vol. 96, 1995. | MR 1245492 | Zbl 0789.76002

[16] L. Onsager, Statistical hydrodynamics, Supplemento al Nuovo Cimento, Vol. 6, 1949, pp. 279-287. | MR 36116

[17] S. Schochet, The point vortex method for periodic weak solutions of the 2-D Euler equations, Comm. Pure Appl. Math., Vol. 49, 9, 1996, pp. 911-965. | MR 1399201 | Zbl 0862.35092