Welcome to Laurent Saloff-Coste's  web page (last updated  December 2008)

     Bienvenue!

• Potential Analysis  (Edior in Chief) : For instructions on how to submit a paper,  go to http://pota.edmgr.com or  click here
  
• Mathematische Zeitschrift (Editor): See  instructions for authors . You can send me manuscript (in pdf or postscript) via email.
• Probability Theory and Related Fields (Editor): See instructions for authors
  
• Journal of Theoretical Probability (Editor): See instructions for authors
  

Teaching:

• Office hours:   MT 567.
  

Research interests:

• Random walks on groups.
• Analysis and potential theory on manifolds. Heat equation, heat diffusion and heat kernel.
• Analysis and potential theory on Lie groups and  locally compact groups. Convolution semigroups.
• Dirichlet forms. Associated Markov processes and geometries.
  
• Finite Markov chains. Quantitative analysis of ergodic Markov chains.

• Probability on groups: Random walks and invariant diffusions, Notices of  the American Mathematical Society. pdf-file
• Random walks on finite groups. Probability on discrete structures, 263--346, Encyclopaedia Math. Sci., 110, Springer, Berlin, 2004. Harry Kesten, Editor. pdf file
• Analysis on Riemannian co-compact covers. Surveys in differential geometry. Vol. IX, 351--384, Surv. Differ. Geom., IX, Int. Press, pdf file
• The heat kernel and its estimates. (1st MJS-SI) Advanced Studies in Pure Mathematics, 2009. pdf file
  
• Sobolev Inequalities in Familiar and Unfamilar settings. Sobolev Spaces in Matehmatics I,  International Series in Mathematics , Springer, Berlin 2009,  Vladimir Maz'ya, Editor.  pdf file
• Central Gaussian convolution semigroups on compact groups: asurveys. Infinite Dimensional Analysis, Quantum Probability and Related Topics 6, 2003. With A. Bendikov.  pdf file
• Brownian motion on compact groups in infinite diomension.   Heat kernels and analysis on manifolds, graphs, and metric spaces (Paris, 2002), 41--63, Contemp. Math., 338, Amer. Math. Soc., Providence, RI, 2003. With A. Bendikov. pdf.file
  

• Spaces of smooth functions and distributions on infinite-dimensional compact groups. J. Funct. Anal. 218 (2005), 168--218, with A. Bendikov.
• Transition operators on co-compact $G$-spaces. Revista Matematica Iberoamericana 22 (2006), 747--799. With W. Woess. pdf file
• Connected Lie groups and property RD. Duke Mathematical Journal 137 (2007), 511--536. With I. Chatterji and C. Pittet. pdf file
• Computations of spectral radii on G-spaces.  Contemporary Mathematics  (Conference on the occasion of  Prof. Sunada's 60th birthday , Nagoya 2007). With W. Woess.  pdf file
• Holomorphic functions and subelliptic heat kernels over Lie groups. To appear in J. Europ. Math. Soc. With B. Driver and L. Gross. pdf file
• Surjectivity of the Taylor map for complex nilpotent Lie groups. Math. Proc. Camb. Phil. Soc. 146 (2008) 177-195. With B. Driver and L. Gross.  pdf file
• Growth of Taylor coefficients over complex homogeneous spaces.  Submitted.  With B. Driver and L. Gross. pdf file
• Sobolev inequalities in familiar and unfamiliar settings. In ``Sobolev Spaces in Mathematics I,  International Mathematical Series, Volume 8, Springer, (V. Maz'ya, Ed.).  pdf file
  
• Pseudo-Poincar\'e Inequalities and Applications to Sobolev Inequalities.  Volume in honor of V. Maz'ya, International Mathematical Series,  Springer, (A. Laptev, Ed.) . pdf file
  

• On the regularity of sample paths of sub-elliptic diffusions on manifolds, Osaka J. Math. 42 (2005), 677--722, with A. Bendikov. pdf file
  
• Ultracontractivity and embedding into $L\sp \infty$. Mathematischen Annalen 337 (2007), 817--853. With A. Bendikov and T. Coulhon. pdf file
  
• Small time heat kernel behavior on Riemannian complexes. New York Journal of Mathematics 4 (2008) 1-37. pdf file
  

• Stability results for  Harnack inequalities, Ann. Inst. Fourier 55 (2005), 825--890, with A. Grigor'yan. zipped.ps-file 
  
• Heat kernel on manifolds with ends, Ann. Inst. Fourier, to appear, with A. Grigor'yan. pdf file
• Neumann and Dirichlet Heat kernels in Inner Uniform Domains, with P. Gyrya. pdf file
  

• Cut-offs for birth and death chains. The Annals of Applied Probability 16 (2006), 2098--2122. With P. Diaconis. pdf file
  
•  Gibbs Sampling, Exponential Families and Orthogonal Polynomials. Statistical Science 23 (2008), 151-173. With P. Diaconis and K. Khare. pdf file
• Convergence of some time inhomogeneous Markov chains via spectral techniques, Stochastic Processes and their Applications
  Volume 117, Pages 961-979. With J. Zuniga. pdf file
  
• Refined estimates for some basic random walks on the symmetric and alternating groups. Alea 4 (2008) 359-392. pdf file
• The cutoff Phenomenon for randomized riffle shuffles. Random Structures and Algorithms 32 (2008)  349--374. With G.Y. Chen.  pdf file 
  
• The cutoff phenomenon for ergodic Markov processes. Electronic Journal of Probability 13 (2008) 26--78. With G.Y. Chen. pdf file
  

• 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.

• Andrzej Zuk   (December 1996, Toulouse)  Sur certaines propriétés spectrales du Laplacien sur les graphes. webpage
  
• Pascal Lezaud   (March 1998, Toulouse) Sur les déviations de la moyenne empirique le long d'une trajectoire d'une  chaine de Markov. webpage
  
• Sandrine Roussel    (June 1999, Toulouse)  Marches aléatoires sur le groupe symétrique.
• Sebastien Blachère   (December 2000, Toulouse)  Agrégation limitée par diffusion interne et temps de coupure sur les groupes discrets à coissance polynomiale. webpage
  
• David Revelle   (June 2002, Cornell)  Random walks on solvable groups.
• Lee Gibson  (June 2005, Cornell) The number of sites visited by a random walk on an infinite graph. webpage
  
• Sharad Goel (June 2005, Cornell) Estimating mixing times: techniques and applications. webpage
  
• Guan-Yu Chen (June 2006, Cornell)  The cut-off phenomenon for finite Markov chains. webpage
  
• Melanie Pivarski (July 2006, Cornell) Heat kernels on Euclidean complexes. webpage
  
• Evgeniy Klebanov (October 2006, Cornell) Asymptotic behavior of convolutions of centered density on Lie groups of polynomial volume growth .
• Pavel Gyrya (June 2007, Cornell)  Heat kernel estimates for inner uniform subsets of Harnack-type Dirichlet spaces.
• Jessica Zuniga (June 2008, Cornell) Merging of some time homogeneous and inhomogeneous Markov chains.