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Coulhon, Th.; Saloff-Coste, L.

Lower bounds for one-dimensional Markov chains. (Minorations pour les chaînes de Markov unidimensionnelles.) (French) Zbl 0792.60063

Probab. Theory Relat. Fields 97, No. 3, 423-431 (1993).
We prove a space-time lower estimate for reversible random walks on graphs having linear growth. This estimate complements a similar upper bound that follows from a work of W. Hebisch and L. Saloff- Coste [Ann. Probab. 21, No. 2, 673-709 (1993; Zbl 0776.60086)].
Reviewer: Th.Coulhon

Cited in 1 Review
Cited in 7 Documents

MSC:

60G50 Sums of independent random variables; random walks
31C20 Discrete potential theory

Keywords:

space-time lower estimate; reversible random walks; upper bound

Citations:

Zbl 0776.60086
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\textit{Th. Coulhon} and \textit{L. Saloff-Coste}, Probab. Theory Relat. Fields 97, No. 3, 423--431 (1993; Zbl 0792.60063)
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References:

[1] Aronson, D. G., Bounds for the fundamental solution of a parabolic equation, Bull. Am. Math. Soc., 73, 890-896 (1967) · Zbl 0153.42002
[2] Carlen, E.; Kusuoka, S.; Stroock, D., Upper bounds for symmetric Markov transition functions, Ann. Inst. Henri Poincaré, Probab. Stat., 23, 245-287 (1987) · Zbl 0634.60066
[3] Coulhon, Th., Inégalités de Gagliardo-Nirenberg pour les semi-groupes d’opérateurs et applications, Potential Anal., 1, 343-353 (1992) · Zbl 0768.47018
[4] Coulhon, Th.; Saloff-Coste, L., Marches aléatoires non symétriques sur les groupes unimodulaires, C.R. Acad. Sci., Paris, Sér. I, 310, 627-630 (1990) · Zbl 0748.60008
[5] Coulhon, Th.; Saloff-Coste, L., Puissances d’un opérateur régularisant, Ann. Inst. Henri Poincaré, Probab. Stat., 26, 176-199 (1991)
[6] Coulhon, Th.; Saloff-Coste, L., Isopérimétrie pour les groupes et les variétés, Rev. Mat. Iberoam., 9, 2, 293-314 (1993) · Zbl 0782.53066
[7] Feller, W., An introduction to probability theory and its applications, vol. I (1968), New York: Wiley, New York · Zbl 0155.23101
[8] Hebisch, W.; Saloff-Coste, L., Gaussian estimates for Markov chains and random walks on groups, Ann. Probab., 21, 2, 673-709 (1993) · Zbl 0776.60086
[9] Saloff-Coste, L., A note on Poincaré, Sobolev and Harnack inequalities, Duke Math. J., 65, 27-38 (1992) · Zbl 0769.58054
[10] Varopoulos, N., Brownian motion and random walks on manifolds, Ann. Inst. Fourier, 34, 243-269 (1984) · Zbl 0523.60071
[11] Varopoulos, N., Isoperimetric inequalities and Markov chains, J. Funct. Anal., 63, 215-239 (1985) · Zbl 0573.60059
[12] Varopoulos, N.; Saloff-Coste, L.; Coulhon, Th., Analysis and geometry on groups (1993), Cambridge: Cambridge University Press, Cambridge · Zbl 1179.22009
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