Laurent Saloff-Coste – Welcome to my webpage – Bienvenue!
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Abram Rogers Bullis Professor of Mathematics office: 567 Malott Hall |
Mail address: Department of Mathematics 567 Malott Hall, Cornell University Ithaca, NY 14853-4201, USA
Some Available Publications
Unpublished
A survey on the relationships between volume growth, isoperimetry, and the behavior of simple random walk on Cayley graphs, with examples, with C. Pittet . This is an unfinis hed manuscript (likely never to be finished). survey.pdf
Most Popular
A note on Poincaré, Sobolev, and Harnack Inequalities Internat. Math. Res. Notices 199 2, no. 2, 27–38. pdf
Logarithmic Sobolev inequalities for finite Markov chains. Ann. Appl. Probab. 6 (1996) , no. 3, 695–750. (with P. Diaconis) pdf
Uniformly elliptic operators on Riemannian manifolds. J. Differential Geom. 36 (1992), no. 2, 417–450. pdf
Sobolev inequalities in disguise. Indiana Univ. Math. J. 44 (1995), no. 4, 1033–1074. (with Bakry, Coulhon and Ledoux) pdf
Comparison theorems for reversible Markov chains. Ann. Appl. Probab. 3 (1993), no. 3, 696–730. (with P. Diaconis) pdf
Gaussian estimates for Markov chains and random walks on groups. Ann. Probab. 21 (1993 ), no. 2, 673–709, (with W. Hebisch) pdf
Isopérimétrie pour les groupes et les variétés. Rev. Mat. Iberoamericana 9 (1993), no. 2, 293–314. (with T. Coulhon) pdf
Variétés riemanniennes isométriques à l'infini. Rev. Mat. Iberoamericana 11 (1995), no. 3, 687–726. (with T. Coulhon) inf-rev.pdf pdf
Surveys
Analysis on Riemannian co-compact covers. Surveys in differential geometry. Vol. IX, 351–384, Surv. Differ. Geom., IX, Int. Press, Somerville, MA, 2004, pdf
Probability on groups: random walks and invariant diffusions. Notices Amer. Math. Soc. 48 (2001), no. 9, 968–977. pdf
Central Gaussian convolution semigroups on compact groups: a survey. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 6 (2003), no. 4, 629–659. pdf
Sobolev inequalities in familiar and unfamiliar settings. Sobolev spaces in mathematics. I, 299–343, Int. Math. Ser. (N. Y.), 8, Springer, New York, 2009. pdf
Pseudo-Poincaré inequalities and applications to Sobolev inequalities. Around the research of Vladimir Maz'ya. I, 349–372, Int. Math. Ser. (N. Y.), 11, Springer, New York, 2010. pdf
Analysis on compact Lie groups of large dimension and on connected compact groups. Colloq. Math. 118 (2010), no. 1, 183–199. pdf
Merging and stability for time inhomogeneous finite Markov chains. Surveys in stochastic processes, 127–151, EMS Ser. Congr. Rep., Eur. Math. Soc., Zürich, 2011. With J. Zúñiga. pdf
Random walks on finite groups. Probability on discrete structures, 263–346, Encyclopaedia Math. Sci., 110, Springer, Berlin, 2004. pdf
On Random Walks
Gaussian estimates for Markov chains and random walks on groups. Ann. Probab. 21 (1993), no. 2, 673–709, (with W. Hebisch) pdf
On random walks on wreath products. Ann. Probab. 30 (2002), no. 2, 948–977. (with C. Pittet) pdf
On the stability of the behavior of random walks on groups. J. Geom. Anal. 10 (2000), no. 4, 713–737. (with C. Pittet) pdf
Random walks on finite rank solvable groups. J. Eur. Math. Soc. (JEMS) 5 (2003), no. 4, 313–342 (with C. Pittet) pdf
Transition operators on co-compact G-spaces. Rev. Mat. Iberoam. 22 (2006), no. 3, 747–799. (with W. Woess) pdf
Random walks driven by low moment measures. Annals of Probab. 40 (2012) 2539–2588. With A. Bendikov. pdf
Random walks on free solvable groups. Math. Z. 279 (2015), 811–848. With Tianyi Zheng pdf
On Harnack Inequalities
A note on Poincaré, Sobolev, and Harnack inequalities. Internat. Math. Res. Notices 1992, no. 2, 27–38. pdf
Uniformly elliptic operators on Riemannian manifolds. J. Differential Geom. 36 (1992), no. 2, 417–450. pdf
On the relation between elliptic and parabolic Harnack inequalities. Ann. Inst. Fourier (Grenoble) 51 (2001), no. 5, 1437–1481. (with W. Hebisch) pdf
Harnack inequality and hyperbolicity for subelliptic-Laplacians with applications to Picard type theorems. Geom. Funct. Anal. 11 (2001), no. 6, 1139–1191. (with T. Coulhon and I. Holopainen) pdf
Opérateurs uniformément sous-elliptiques sur les groupes de Lie. J. Funct. Anal. 98 (1991), no. 1, 97–121. (with D. Stroock) pdf
Stability results for Harnack inequalities. Ann. Inst. Fourier (Grenoble) 55 (2005), no. 3, 825–890. (with A. Grigoryan) pdf
Heat kernel on manifolds with ends. Ann. Inst. Fourier (Grenoble) 59 (2009), no. 5, 1917–1997. (with A. Grigoryan) pdf
On Dirichlet forms on complexes
Small time heat kernel behavior on Riemannian complexes. New York J. Math. 14 (2008), 459–494. (with M. Pivarski) pdf
The heat semigroup and Brownian motion on strip complexes. Adv. Math. 226 (2011), no. 1, 992–1055. (with A. Bendikov, M. Salvatori and W. Woess) pdf
On finite Markov chains
Comparison techniques for random walk on finite groups. Ann. Probab. 21 (1993), no. 4, 2131–2156. (with P. Diaconis) pdf
What do we know about the Metropolis algorithm? 27th Annual ACM Symposium on the Theory of Computing (STOC’95) (Las Vegas, NV). J. Comput. System Sci. 57 (1998), no. 1, 20–36. (with P. Diaconis) pdf
Nash inequalities for finite Markov chains. J. Theoret. Probab. 9 (1996), no. 2, 459–510. (with P. Diaconis) pdf
Moderate growth and random walk on finite groups. Geom. Funct. Anal. 4 (1994), no. 1, 1–36. (with P. Diaconis) pdf
The cutoff phenomenon for ergodic Markov processes. Electron. J. Probab. 13 (2008), no. 3, 26–78. (with Guan-Yu Chen) pdf
The L2-cutoff for reversible Markov processes. J. Funct. Anal. 258 (2010), no. 7, 2246–2315. (with Guan-Yu Chen) pdf