Birthplace: Arlington, Massachusettes

Employment: 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)

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.