Welcome to Laurent Saloff-Coste's web
page (last updated
August 2007)
Bienvenue!
Laurent Saloff-Coste
Professor, Department of Mathematics, Cornell University
mail address: Department of Mathematics,
Cornell University, Malott Hall, Ithaca, NY, 14853-4201, USA
email: lsc (at) math.cornell.edu
phone: (607) 255 7241
fax: (607) 255 7149
office: 567, Malott Hall
Rollo Davidson award,
1994
Guggenheim fellow, 2006/07
Math778-Spring2008 Finite
Markov Chains
If you signed up the attendence sheet you should be able to get my
Saint-Flour notes by clicking here.
You will need to have your Cornell netid and password.
Editorial
activities:
Teaching:
- Office hours: Monday 11:20-12:20pm
MT 567
Research interests:
- Random walks on finitely generated
groups.
- Analysis and potential theory on
manifolds. Heat diffusion equation and heat kernel.
- Dirichlet forms and potentials
theory on Lie groups and locally compact groups. Gaussian
convolution semigroups.
- Finite Markov chains. Quantitative
analysis of ergodic Markov chains.
Research supported in part by NSF
grant DMS-0102126/DMS and DMS-0603886
Selected recent Publications
- Random walks on finite
groups.
Probability on discrete structures, 263--346, Encyclopaedia
Math. Sci., 110, Springer, Berlin, 2004. Harry Kesten,
Editor. pdf file
- Spaces of smooth
functions and distributions on infinite-dimensional compact groups.
J. Funct. Anal. 218 (2005), 168--218, with A. Bendikov.
- Stability results for Harnack
inequalities, Ann. Inst. Fourier 55 (2005), 825--890, with A.
Grigor'yan. zipped.ps-file
- On the regularity of
sample paths of sub-elliptic diffusions on manifolds, Osaka J.
Math. 42 (2005), 677--722, with A. Bendikov.
- Analysis on Riemannian
co-compact covers. Surveys in differential geometry. Vol.
IX, 351--384, Surv.
Differ. Geom., IX, Int. Press, pdf file
- cut-offs
for birth and death chains. The Annals of Applied Probability 16
(2006), 2098--2122. With P. Diaconis.
- Transition
operators on co-compact $G$-spaces. Revista Matematica
Iberoamericana 22 (2006), 747--799. With W. Woess.
- Ultracontractivity
and embedding into $L\sp \infty$.
Mathematischen Annalen 337 (2007), 817--853. With A. Bendikov and T.
Coulhon.
- Connected
Lie groups and property RD. Duke
Mathematical Journal 137 (2007), 511--536. With I. Chatterji and C.
Pittet.
Other
publications: click here
List of publications: click here
Preprints:
- 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.
Former graduate Students:
- 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.
- Melanie
Pivarski (July 2006, Cornell) Heat kernels on Euclidean
complexes.
- 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.