Harry Kesten

Harry Kesten, 1970.

Harry Kesten (19 November 1931, Germany) is an American mathematician best known for his work in probability, most notably on random walks and percolation theory.

Biography

Kesten grew up in the Netherlands, where he moved with his parents in 1933 to escape the Nazis. He received his Ph.D. in 1956 at Cornell University under supervision of Mark Kac. He was an instructor at Princeton University and the Hebrew University before returning to Cornell where he is now professor emeritus of mathematics.

Mathematical work

Kesten's work includes a number of fundamental contributions, including the following.

• Showing that amenability is equivalent to zero spectral gap and that a regular tree of degree has spectral radius ^[1]
• His work with Hillel Furstenberg on products of random matrices^[2]
• Enumerations of self-avoiding walks and a "pattern theorem".^[3][4]
• Resolving a conjecture of Erdős and Szűsz on the discrepancy of irrational rotations^[5]
• Kesten did much work on percolation including proving that the critical probability of bond percolation on the square lattice equals 1/2,^[6] demonstrating the so-called scaling relations^[7] and writing the first book on percolation directed towards mathematicians.^[8]
• Giving an upper bound for the growth of arms in diffusion-limited aggregation^[9]
• His work with Vladas Sidoravicius on the spread of an infection in a moving population^[10][11]

Awards and honors

Kesten was a Guggenheim fellow, Alfred P. Sloan Fellow, received the Brouwer Medal in 1981, the Steele Prize^[12] for Lifetime Achievement from the AMS, and the George Pólya Prize from the SIAM. He is also a member of the National Academy of Sciences and a correspondent member of the Royal Netherlands Academy of Arts and Sciences.^[13] In 2012 he became a fellow of the American Mathematical Society.^[14]

Selected works

• with Mark Kac: "On rapidly mixing transformations and an application to continued fractions". Bull. Amer. Math. Soc. 64 (5): 283–287. 1958. doi:10.1090/s0002-9904-1958-10226-8. MR 0097114; correction 65 1958 p. 67 
• "Symmetric random walks on groups". Trans. Amer. Math. Soc. 92: 336–354. 1959. doi:10.1090/s0002-9947-1959-0109367-6. MR 0109367. 
• "Occupation times for Markov and semi-Markov chains". Trans. Amer. Math. Soc. 103: 82–112. 1962. doi:10.1090/s0002-9947-1962-0138122-6. MR 0138122. 
• Some probabilistic theorems on Diophantine approximations. Trans. Amer. Math. Soc. 103. 1962. pp. 189–217. doi:10.1090/s0002-9947-1962-0137692-1. MR 0137692. 
• with Zbigniew Ciesielski: A limit theorem for the fractional parts of the sequence {2^kt}. Proc. Amer. Math. Soc. 13. 1962. pp. 596–600. doi:10.1090/s0002-9939-1962-0138612-1. MR 0138612. 
• with D. Ornstein and F. Spitzer: "A general property of random walk". Bull. Amer. Math. Soc. 68 (5): 526–528. 1962. doi:10.1090/s0002-9904-1962-10808-8. MR 0142160. 
• "A convolution equation and hitting probabilities of single points for processes with stationary independent increments". Bull. Amer. Math. Soc. 75 (3): 573–578. 1969. doi:10.1090/s0002-9904-1969-12245-7. MR 0251797. 
• "Some linear stochastic growth models". Bull. Amer. Math. Soc. 77 (4): 492–511. 1971. doi:10.1090/s0002-9904-1971-12732-5. MR 0278404. 
• Hitting probabilities for single points for processes of stationary independent increments. Memoirs of the AMS; 93. Providence, R.I.: AMS. 1969. 
• "Sums of stationary sequences cannot grow slower than linearly". Proc. Amer. Math. Soc. 49: 205–211. 1975. doi:10.1090/s0002-9939-1975-0370713-4. MR 0370713. 
• "Erickson's conjecture on the rate of d-dimensional random walk". Trans. Amer. Math. Soc. 240: 65–113. 1978. doi:10.1090/s0002-9947-1978-0489585-x. MR 489585. 
• Percolation theory for mathematicians. Stuttgart: Birkhäuser. 1982. ISBN 3-7643-3107-0. ^[15]
• "What is Percolation?" (PDF). Notices AMS. 2006. 

See also

• Amenable group

References

External links

• Harry Kesten at the Mathematics Genealogy Project
• Department webpage
• Mini-biography