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Unpublished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 (likely never to be finished). Survey 

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)  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 

• Heat kernel estimates on Harnack manifolds and beyond. International Congress of Mathematicians 2022, European Mathematical Society Press (2023), Volume VI, 4452--4473. pdf 

On Random Walks 

• 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

• 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 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