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1994 | 67 | 1 | 109-121
Tytuł artykułu

Convergence to equilibrium and logarithmic Sobolev constant on manifolds with Ricci curvature bounded below

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Rocznik
Tom
67
Numer
1
Strony
109-121
Opis fizyczny
Daty
wydano
1994
otrzymano
1993-07-07
poprawiono
1993-11-03
Twórcy
  • Laboratoire de Statistique et Probabilités, Université Paul Sabatier, 118, Route de Narbonne, 31062 Toulouse Cedex, France
Bibliografia
  • [1] D. Aldous and P. Diaconis, Strong uniform times and finite random walks, Adv. Appl. Math. 8 (1987), 69-97.
  • [2] D. Bakry, L'hypercontractivité et son utilisation en théorie des semigroupes, in: Ecole d'été de Saint Flour, 1992.
  • [3] R. Brooks, On the spectrum of non-compact manifolds with finite volume, Math. Z. 187 (1984), 425-432.
  • [4] R. Brooks, The spectral geometry of tower of coverings, J. Differential Geom. 23 (1986), 97-107.
  • [5] R. Brooks, Combinatorial problems in spectral geometry, in: Lecture Notes in Math. 1201, Springer, 1988, 14-32.
  • [6] P. Buser, B. Colbois and J. Dodziuk, Tubes and eigenvalues for negatively curved manifolds, J. Geom. Anal. 3 (1993), 1-26.
  • [7] J. Cheeger, M. Gromov and M. Taylor, Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds, J. Differential Geom. 17 (1982), 15-53.
  • [8] S. Cheng, Eigenvalue comparison theorems and its geometric applications, Math. Z. 143 (1975), 289-297.
  • [9] Th. Coulhon et L. Saloff-Coste, Variétés Riemanniennes isométriques à l'infini, preprint, 1993.
  • [10] J.-D. Deuschel and D. Stroock, Large Deviations, Academic Press, Boston, 1989.
  • [11] P. Diaconis, Group Representations in Probability and Statistics, IMS, Hayward, CA, 1988.
  • [12] P. Diaconis and L. Saloff-Coste, An application of Harnack inequality to random walk on finite nilpotent quotients, preprint, 1993.
  • [13] P. Diaconis and L. Saloff-Coste, Logarithmic Sobolev inequality for finite Markov chains, preprint, 1992.
  • [14] M. Gromov, Groups of polynomial growth and expanding maps, Publ. IHES 53 (1980).
  • [15] L. Gross, Logarithmic Sobolev inequalities, Amer. J. Math. 97 (1975), 1061-1083.
  • [16] R. Holley and D. Stroock, Uniform and $L^2$ convergence in one dimensional stochastic Ising models, Comm. Math. Phys. 123 (1989), 85-93.
  • [17] D. Kazhdan, Connection of the dual space of a group with the structure of its closed subgroups, Functional Anal. Appl. 1 (1968), 63-65.
  • [18] P. Li and S.-T. Yau, Estimates of eigenvalues of a compact Riemannian manifold, in: Proc. Sympos. Pure Math. 36, Amer. Math. Soc., 1980, 205-239.
  • [19] P. Li and S.-T. Yau, On the parabolic kernel of the Schrödinger operator, Acta Math. 156 (1986), 153-201.
  • [20] A. Lubotzky, Discrete Groups, Expanding Graphs and Invariant Measures, forthcoming monograph.
  • [21] L. Payne and H. Weinberger, An optimal Poincaré inequality for convex domains, Arch. Rational Mech. Anal. 5 (1960), 286-292.
  • [22] O. Rothaus, Diffusion on compact Riemannian manifolds and logarithmic Sobolev inequalities, J. Funct. Anal. 42 (1981), 102-109.
  • [23] O. Rothaus, Hypercontractivity and the Bakry-Emery criterion for compact Lie groups, ibid. 65 (1986), 358-367.
  • [24] L. Saloff-Coste, Uniformly elliptic operators on Riemannian manifolds, J. Differential Geom. 36 (1992), 417-450.
  • [25] L. Saloff-Coste, A note on Poincaré, Sobolev and Harnack inequalities, Duke Math. J. 65 (1992), IMRN, 27-38.
  • [26] L. Saloff-Coste, Quantitative bounds on the convergence of diffusion semigroups to equilibrium, Math. Z., to appear.
  • [27] P. Sarnack, Some Applications of Modular Forms, Cambridge University Press, 1991.
  • [28] D. Stroock and B. Zegarlinski, The equivalence of the logarithmic Sobolev inequality and the Dobrushin-Shlosman mixing condition, Comm. Math. Phys. 144 (1992), 303-323.
  • [29] N. Varopoulos, Une généralisation du théorème de Hardy-Littlewood-Sobolev pour les espaces de Dirichlet, C. R. Acad. Sci. Paris Sér. I 299 (1984), 651-654.
  • [30] N. Varopoulos, L. Saloff-Coste and Th. Coulhon, Analysis and Geometry on Groups, Cambridge University Press, 1993.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv67i1p109bwm
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