Carl Graham

Born:

place: Arlington, Massachusettes

University of Paris 6 (equivalent BS); École Normale Superieure (equivlaent Masters)

Ph.D. University
of Paris 6

thesis:

Professor at the Centre National pour la Recherche Scientifique (CNRS) at the École Polytechnique, Palaiseau , France (CNRS is loosely translated into France's National Center for Scientific Research)

personal or universal URL:

email:

Carl Graham was born in the U.S. but when he was six his father Eugene Alexander Graham, Jr., a mathematician, moved away from a rascist U.S.A. to France, where Carl was raised. Carl's undergraduate education occured at Ecole Normale Superieure (Paris) and Universite Paris 6 (Paris). He received his Masters degree in Mathematics from École Normale Superieure (Paris) and his Ph.D. (1984?) in Probability from Universite Paris 6 (Paris).

Research

Dr. Graham has written at least 17 papers on Applied Probability:

17. **Graham, C.**; Méléard,
S. *A large deviation principle for a large star-shaped loss
network with links of capacity one *. Statistical mechanics
of large networks (Rocquencourt, 1996). Markov Process. Related
Fields **3** (1997), no. 4, 475--492.

16. **Graham, C.**; Méléard,
S. *An upper bound of large deviations for a generalized star-shaped
loss network *. Markov Process. Related Fields **3** (1997),
no. 2, 199--223.

15. **Graham, Carl**; Méléard,
Sylvie *Stochastic particle approximations for generalized Boltzmann
models and convergence estimates *. Ann. Probab. **25**
(1997), no. 1, 115--132.

14. **Graham, C.**; Kurtz, Th. G.; Méléard,
S.; Protter, Ph. E.; Pulvirenti, M.; Talay, D. *Probabilistic
models for nonlinear partial differential equations *. Lectures
given at the 1st Session and Summer Schoolheld in Montecatini
Terme, May 22--30, 1995. Edited by Talay and L. Tubaro. Lecture
Notes in Mathematics, **1627**. Fondazione C.I.M.E.. [C.I.M.E.
Foundation] Springer-Verlag, Berlin; Centro Internazionale Matematico
Estivo (C.I.M.E.), Florence, 1996. x+301 pp. ISBN: 3-540-61397-8
60-06 (00B25)

13. **Graham, Carl**; Méléard,
Sylvie *Convergence rate on path space for stochastic particle
approximations to the Boltzmann equation *.ICIAM/GAMM 95 (Hamburg,
1995). Z. Angew. Math. Mech. **76** (1996), suppl. 1, 291--294.

12. **Graham, Carl** *A statistical physics
approach to large networks *. Probabilistic models for nonlinear
partial differential equations(Montecatini Terme, 1995), 127--147,
Lecture Notes in Math., **1627**, Springer, Berlin, 1996.

11. **Graham, Carl**; Méléard,
Sylvie *Dynamic asymptotic results for a generalized star-shaped
loss network *. Ann. Appl. Probab. **5** (1995), no. 3,
666--680.

10. **Graham, Carl **__Homogenization and
propagation of chaos to a nonlinear diffusion with sticky reflection__.
Probab. Theory Related Fields **101** (1995), no. 3, 291--302.

9. **Graham, Carl**; Méléard,
Sylvie __Fluctuations for a fully connected loss network with
alternate routing__. Stochastic Process. Appl. **53** (1994),
no. 1, 97--115.

8. **Graham, Carl**; Méléard,
Sylvie *C*__haos hypothesis for a system interacting through
shared resources__. Probab. Theory Related Fields **100**
(1994), no. 2, 157--173.

7. **Graham, Carl**; Méléard,
Sylvie __Propagation of chaos for a fully connected loss network
with alternate routing__. Stochastic Process. Appl. **44**
(1993), no. 1, 159--180.

6. **Graham, Carl** __Nonlinear diffusion
with jumps__. Ann. Inst. H. Poincaré Probab. Statist.
**28** (1992), no. 3, 393--402.

5. **Graham, Carl**; McKean-Vlasov Itô-*S*__korohod
equations, and nonlinear diffusions with discrete jump sets__.
Stochastic Process. Appl. **40** (1992), no. 1, 69--82.

4. **Graham, Carl** __Nonlinear limit for
a system of diffusing particles which alternate between two states__.
Appl. Math. Optim. **22** (1990), no. 1, 75--90.

3. **Graham, Carl**; Métivier, Michel
__System of interacting particles and nonlinear diffusion reflecting
in a domain with sticky boundary__. Probab. Theory Related Fields
**82** (1989), no. 2, 225--240.

2. **Graham, Carl** __The martingale problem
with sticky reflection conditions, and a system of particles interacting
at the boundary__. Ann. Inst. H. Poincaré Probab. Statist.
**24** (1988), no. 1, 45--72.

1. **Graham, Carl** __Boundary processes:
the calculus of processes diffusing on the boundary__. Ann.
Inst. H. Poincaré Probab. Statist. **21** (1985), no.
1, 73--102.

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