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Volumn 324, Issue 3, 2002, Pages 521-556

Harnack inequalities and sub-Gaussian estimates for random walks

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EID: 0036981648     PISSN: 00255831     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00208-002-0351-3     Document Type: Article
Times cited : (80)

References (38)
  • 1
    • 0002163683 scopus 로고    scopus 로고
    • Diffusions on fractals
    • Lectures on Probability Theory and Statistics, Ecole d'été de Probabilités de Saint-Flour XXV - 1995, Springer
    • Barlow, M.T.: Diffusions on fractals. In: Lectures on Probability Theory and Statistics, Ecole d'été de Probabilités de Saint-Flour XXV - 1995, Lecture Notes Math. 1690, Springer, 1998. 1-121
    • (1998) Lecture Notes Math. , vol.1690 , pp. 1-121
    • Barlow, M.T.1
  • 3
    • 0001035130 scopus 로고
    • The construction of the Brownian motion on the Sierpisnki carpet
    • Barlow, M. T., Bass, R. F.: The construction of the Brownian motion on the Sierpisnki carpet. Ann. Inst. H. Poincaré, 25 (1989) 225-257
    • (1989) Ann. Inst. H. Poincaré , vol.25 , pp. 225-257
    • Barlow, M.T.1    Bass, R.F.2
  • 4
    • 0000869325 scopus 로고
    • Transition densities for Brownian motion on the Sierpinski carpet
    • Barlow, M. T., Bass, R. F.: Transition densities for Brownian motion on the Sierpinski carpet. Probab. Th. Rel. Fields, 91 (1992) 307-330
    • (1992) Probab. Th. Rel. Fields , vol.91 , pp. 307-330
    • Barlow, M.T.1    Bass, R.F.2
  • 5
    • 0033465207 scopus 로고    scopus 로고
    • Brownian motion and harmonic analysis on Sierpinski carpets
    • Barlow, M. T., Bass, R. F.: Brownian motion and harmonic analysis on Sierpinski carpets. Canad. J. Math., 54 (1999) 673-744
    • (1999) Canad. J. Math. , vol.54 , pp. 673-744
    • Barlow, M.T.1    Bass, R.F.2
  • 6
    • 0013125524 scopus 로고    scopus 로고
    • Random walks on graphical Sierpinski carpets
    • Random walks and discrete potential theory (Cortona, Italy, 1997), Ed. Picardello, M., Woess, W., Cambridge Univ. Press, Cambridge
    • Barlow, M. T., Bass, R. F.: Random walks on graphical Sierpinski carpets. In: Random walks and discrete potential theory (Cortona, Italy, 1997), Ed. Picardello, M., Woess, W., Symposia Math. 39, Cambridge Univ. Press, Cambridge, 1999. 26-55
    • (1999) Symposia Math. , vol.39 , pp. 26-55
    • Barlow, M.T.1    Bass, R.F.2
  • 7
    • 0035608868 scopus 로고    scopus 로고
    • Manifolds and graphs with slow heat kernel decay
    • Barlow, M. T., Coulhon, T., Grigor'yan, A.: Manifolds and graphs with slow heat kernel decay. Invent. Math., 144 (2001) 609-649
    • (2001) Invent. Math. , vol.144 , pp. 609-649
    • Barlow, M.T.1    Coulhon, T.2    Grigor'Yan, A.3
  • 8
    • 0000835875 scopus 로고
    • Brownian motion on the Sierpinski gasket
    • Barlow, M.T., Perkins, E.A.: Brownian motion on the Sierpinski gasket. Probab. Th. Rel. Fields, 79 (1988) 543-623
    • (1988) Probab. Th. Rel. Fields , vol.79 , pp. 543-623
    • Barlow, M.T.1    Perkins, E.A.2
  • 11
    • 0030295841 scopus 로고    scopus 로고
    • Ultracontractivity and Nash type inequalities
    • Coulhon, T.: Ultracontractivity and Nash type inequalities. J. Funct. Anal., 141 (1996) no.2, 510-539
    • (1996) J. Funct. Anal. , vol.141 , Issue.2 , pp. 510-539
    • Coulhon, T.1
  • 12
    • 0032382061 scopus 로고    scopus 로고
    • Random walks on graphs with regular volume growth
    • Coulhon T., Grigor'yan, A.: Random walks on graphs with regular volume growth. Geom. and Funct. Analysis, 8 (1998) 656-701
    • (1998) Geom. and Funct. Analysis , vol.8 , pp. 656-701
    • Coulhon, T.1    Grigor'Yan, A.2
  • 13
    • 0033481532 scopus 로고    scopus 로고
    • Parabolic Harnack inequality and estimates of Markov chains on graphs
    • Delmotte, T.: Parabolic Harnack inequality and estimates of Markov chains on graphs. Revista Matemática Iberoamericana, 15 (1999) no.1, 181-232
    • (1999) Revista Matemática Iberoamericana , vol.15 , Issue.1 , pp. 181-232
    • Delmotte, T.1
  • 14
    • 0000472452 scopus 로고
    • On the motion of small particles suspended in liquids at rest required by the molecular-kinetic theory of heat
    • Einstein, A.: On the motion of small particles suspended in liquids at rest required by the molecular-kinetic theory of heat. Annalen der Physik, 1905. See also "Einstein's miraculous year", Ed. Stachel, J., Princeton University Press, 1998. 71-85
    • (1905) Annalen der Physik , pp. 71-85
    • Einstein, A.1
  • 15
    • 0003408049 scopus 로고    scopus 로고
    • Princeton University Press
    • Einstein, A.: On the motion of small particles suspended in liquids at rest required by the molecular-kinetic theory of heat. Annalen der Physik, 1905. See also "Einstein's miraculous year", Ed. Stachel, J., Princeton University Press, 1998. 71-85
    • (1998) Einstein's Miraculous Year
    • Stachel, J.1
  • 16
    • 33646917618 scopus 로고
    • A new proof of Moser's parabolic Harnack inequality via the old ideas of Nash
    • Fabes E.B., Stroock D.W. A new proof of Moser's parabolic Harnack inequality via the old ideas of Nash. Arch. Rat. Mech. Anal., 96 (1986) 327-338
    • (1986) Arch. Rat. Mech. Anal. , vol.96 , pp. 327-338
    • Fabes, E.B.1    Stroock, D.W.2
  • 17
  • 19
    • 0002209819 scopus 로고
    • The heat equation on non-compact Riemannian manifolds
    • Grigor'yan, A.: The heat equation on non-compact Riemannian manifolds. (in Russian) Matem. Sbornik, 182 (1991) no.1, 55-87 Engl. transl. Math. USSR Sb., 72 (1992) no.1, 47-77
    • (1991) Matem. Sbornik , vol.182 , Issue.1 , pp. 55-87
    • Grigor'yan, A.1
  • 20
    • 84956103754 scopus 로고
    • Engl. transl.
    • Grigor'yan, A.: The heat equation on non-compact Riemannian manifolds. (in Russian) Matem. Sbornik, 182 (1991) no.1, 55-87 Engl. transl. Math. USSR Sb., 72 (1992) no.1, 47-77
    • (1992) Math. USSR Sb. , vol.72 , Issue.1 , pp. 47-77
  • 21
    • 0001436849 scopus 로고
    • Heat kernel upper bounds on a complete non-compact manifold
    • Grigor'yan, A.: Heat kernel upper bounds on a complete non-compact manifold. Revista Matemática Iberoamericana, 10 (1994) no.2, 395-452
    • (1994) Revista Matemática Iberoamericana , Issue.2 , pp. 395-452
    • Grigor'yan, A.1
  • 22
    • 0039657135 scopus 로고    scopus 로고
    • Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds
    • Grigor'yan, A.: Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds. Bull. Amer. Math. Soc., 36 (1999) 135-249
    • (1999) Bull. Amer. Math. Soc. , vol.36 , pp. 135-249
    • Grigor'Yan, A.1
  • 23
    • 0033245886 scopus 로고    scopus 로고
    • Heat kernel on connected sums of Riemannian manifolds
    • Grigor'yan, A., Saloff-Coste, L.: Heat kernel on connected sums of Riemannian manifolds. Math. Research Letters, 6 (1999) no. 3-4, 307-321
    • (1999) Math. Research Letters , vol.6 , Issue.3-4 , pp. 307-321
    • Grigor'Yan, A.1    Saloff-Coste, L.2
  • 24
    • 0000763788 scopus 로고    scopus 로고
    • Sub-Gaussian estimates of heat kernels on infinite graphs
    • Grigor'yan, A., Telcs, A.: Sub-Gaussian estimates of heat kernels on infinite graphs. Duke Math. J., 109 (2001) no.3, 452-510
    • (2001) Duke Math. J. , vol.109 , Issue.3 , pp. 452-510
    • Grigor'Yan, A.1    Telcs, A.2
  • 25
    • 0041034140 scopus 로고    scopus 로고
    • On the relation between elliptic and parabolic Harnack inequalities
    • Hebisch, W., Saloff-Coste, L.: On the relation between elliptic and parabolic Harnack inequalities. Ann. Inst. Fourier, 51 (2001) no.5, 1437-1481
    • (2001) Ann. Inst. Fourier , vol.51 , Issue.5 , pp. 1437-1481
    • Hebisch, W.1    Saloff-Coste, L.2
  • 26
    • 0029690374 scopus 로고    scopus 로고
    • Transition probabilities for the simple random walk on the Sierpinski graph
    • Jones O.D.: Transition probabilities for the simple random walk on the Sierpinski graph. Stoch. Proc. Appl., 61 (1996) 45-69
    • (1996) Stoch. Proc. Appl. , vol.61 , pp. 45-69
    • Jones, O.D.1
  • 28
    • 0013202999 scopus 로고
    • Engl. transl. Partial Differential Equations III, Springer
    • Kondrat'ev, V.A., Landis, E. M.: Qualitative theory of linear second-order partial differential equations. (in Russian) Itogi Nauki i Techniki, serija Sovremennye Problemy Matematiki, Fundamental'nye Napravlenija 32, VINITI, Moscow, 1988. 99-215 Engl. transl. In: Partial Differential Equations III, Encyclopedia of Math. Sci. 32, Springer, 1990.
    • (1990) Encyclopedia of Math. Sci. , vol.32
  • 29
    • 0001177888 scopus 로고    scopus 로고
    • Mean value inequalities
    • Li, P., Wang, J.: Mean value inequalities. Indiana Univ. Math. J., 48 (1999) 1257-1283
    • (1999) Indiana Univ. Math. J. , vol.48 , pp. 1257-1283
    • Li, P.1    Wang, J.2
  • 30
    • 0000324115 scopus 로고
    • On the parabolic kernel of the Schrödinger operator
    • Li, P., Yau, S.-T.: On the parabolic kernel of the Schrödinger operator. Acta Math., 156 (1986) no.3-4, 153-201
    • (1986) Acta Math. , vol.156 , Issue.3-4 , pp. 153-201
    • Li, P.1    Yau, S.-T.2
  • 31
    • 84980080977 scopus 로고
    • On Harnack's theorem for elliptic differential equations
    • Moser, J.: On Harnack's theorem for elliptic differential equations. Comm. Pure Appl. Math., 14 (1961) 577-591
    • (1961) Comm. Pure Appl. Math. , vol.14 , pp. 577-591
    • Moser, J.1
  • 32
    • 84980078895 scopus 로고
    • A Harnack inequality for parabolic differential equations
    • Correction: Comm. Pure Appl. Math., 20 (1967) 231-236
    • Moser, J.: A Harnack inequality for parabolic differential equations. Comm. Pure Appl. Math., 17 (1964) 101-134 Correction: Comm. Pure Appl. Math., 20 (1967) 231-236
    • (1964) Comm. Pure Appl. Math. , vol.17 , pp. 101-134
    • Moser, J.1
  • 33
    • 0001680091 scopus 로고
    • Continuity of solutions of parabolic and elliptic equations
    • Nash, J.: Continuity of solutions of parabolic and elliptic equations. Amer. J. Math., 80 (1958) 931-954
    • (1958) Amer. J. Math. , vol.80 , pp. 931-954
    • Nash, J.1
  • 34
    • 84963021360 scopus 로고
    • A note on Poincaré, Sobolev, and Harnack inequalities
    • Internat. Math. Res. Notices, 2
    • Saloff-Coste, L.: A note on Poincaré, Sobolev, and Harnack inequalities. Duke Math. J., 65 no.3, Internat. Math. Res. Notices, 2 (1992) 27-38
    • (1992) Duke Math. J. , vol.65 , Issue.3 , pp. 27-38
    • Saloff-Coste, L.1
  • 35
    • 0001539796 scopus 로고
    • Random walks on graphs, electric networks and fractals
    • Telcs, A.: Random walks on graphs, electric networks and fractals. J. Prob. Th. Rel. Fields, 82 (1989) 435-449
    • (1989) J. Prob. Th. Rel. Fields , vol.82 , pp. 435-449
    • Telcs, A.1
  • 36
    • 0013169256 scopus 로고    scopus 로고
    • Local sub-Gaussian transition probability estimates, the strongly recurrent case
    • Telcs, A.: Local sub-Gaussian transition probability estimates, the strongly recurrent case. to appear in Elec. J. Prob.
    • Elec. J. Prob.
    • Telcs, A.1
  • 37
    • 0035635023 scopus 로고    scopus 로고
    • Volume and time doubling of graphs and random walks, the strongly recurrent case
    • Telcs, A.: Volume and time doubling of graphs and random walks, the strongly recurrent case. to appear in Comm. Pure Appl. Math.
    • Comm. Pure Appl. Math.
    • Telcs, A.1
  • 38
    • 46549093732 scopus 로고
    • Hardy-Littlewood theory for semigroups
    • Varopoulos, N. Th.: Hardy-Littlewood theory for semigroups. J. Funct. Anal., 63 (1985) no.2, 240-260
    • (1985) J. Funct. Anal. , vol.63 , Issue.2 , pp. 240-260
    • Varopoulos, N.Th.1


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