Itai Benjamini
Incumbent of the Louis and Ida Rich Career Development Chair
In 1921 George Polya proved that "a
drunk man will eventually return home but a drunk bird will loose it's way in
space". That is, planar random walk is recurrent, yet random walk in space
is transient. This inspiring (not hard) result is the basic example of a theorem
relating asymptotic behavior of a random process taking place in that space.
One theme of my research is to understand the interplay between geometrical structure and invariants of spaces, such as "the isoperimetric profile", volume growth or hyperbolicity, and properties of some natural random processes and systems living in these spaces. Among the processes, we have: percolation, some variants of random walks and random spanning trees. Some of the spaces we study are geometrical realizations of discrete groups. This point of view led to further understanding of the random processes and also allowed us to obtain purely geometrical results.
Recent Publications
- [with Z.-Q. Chen and S. Rohde] Boundary Trace of Reflecting Brownian Motions. Probability Theory and Related Fields, to appear.
- [with G. Kalai and O. Schramm] First Passage Percolation Has Sublinear Distance Variance. Ann. Prob., to appear.
- [with H. Kesten, Y. Peres and O. Schramm] Geometry of the Uniform Spanning Forest: Transitions in Dimensions 4, 8, 12. Ann. of Math., to appear.