Henry P. McKean Jr. (born May 13 1946) is an American mathematician whose research spans probability theory, analysis, partial differential equations, and mathematical physics. He has held faculty positions at Princeton University, the University of California, Berkeley, and Cornell University, where he is the Albert E. and Carol L. Davis Professor of Mathematics.
Education
- B.A., Princeton University, 1968
- Ph.D., Princeton University, 1972, under the supervision of William Feller.
Research contributions
| Area | Notable work |
|---|---|
| Stochastic processes | Development of the McKean–Vlasov (nonlinear diffusion) equation; introduction of probabilistic methods for solving certain nonlinear PDEs; co‑author of Diffusion Processes and Their Sample Paths (1977) with Kiyosi Itô. |
| Spectral theory & analysis | Results on eigenvalue distributions of random matrices; work on the Bôcher Memorial Prize‑winning research concerning the eigenvalues of Schrödinger operators (awarded 1975). |
| Integrable systems | Study of the Korteweg‑de Vries (KdV) equation using probabilistic techniques; contributions to the theory of solitons. |
| Mathematical physics | Applications of probability to quantum mechanics and statistical mechanics, including the probabilistic representation of solutions to the nonlinear Schrödinger equation. |
| Books and monographs | Stochastic Integrals (1971); Gaussian Processes, Function Theory, and the Geometry of the Space of Paths (1995); Analysis and Geometry for Probability (2011). |
Awards and honors
- Sloan Research Fellow (1972–1975)
- Bôcher Memorial Prize, American Mathematical Society (1975)
- Fellow, American Academy of Arts and Sciences (1991)
- Member, National Academy of Sciences (elected 2002)
Academic service
McKean has served on editorial boards for journals such as Annals of Probability and Communications in Pure and Applied Mathematics. He has also chaired several research programs at the Institute for Advanced Study and the Simons Center for Geometry and Physics.
Personal
Born in New York City, McKean is the son of mathematician H. P. McKean Sr., a noted statistician. He is married and has two children.
Selected publications
- H. P. McKean, Stochastic Integrals, Academic Press, 1971.
- K. Itô & H. P. McKean, Diffusion Processes and Their Sample Paths, Springer, 1977.
- H. P. McKean, Gaussian Processes, Function Theory, and the Geometry of the Space of Paths, Springer, 1995.
- H. P. McKean, Analysis and Geometry for Probability, Cambridge University Press, 2011.
Impact
Henry McKean’s work has bridged deterministic and stochastic analysis, influencing fields ranging from statistical mechanics to financial mathematics. His probabilistic techniques for nonlinear PDEs have become standard tools in modern analysis.
