Laurent Saloff-Coste
Department of Mathematics
College of Arts and Sciences
Department of Mathematics
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Unpublished: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 unfinished manuscript (we still hope to
finish it!). Here is the zipped.ps-file
of the present
version. It will not be updated until the final version is ready.
Most popular:
- A note on Poincaré, Sobolev, and Harnack inequalities.
Internat. Math. Res. Notices 1992, 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) 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
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
On finite Markov chains:
- Comparison techniques for random walk on finite groups.
Ann. Probab. 21 (1993), no. 4, 2131–2156. (with P. Diaconis)
- 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