Christian G. Benes, Graduate Student
Please note: Christian has left the Mathematics department at Duke University; some info here might not be up to date.
- Contact Info:
- Office Hours:
- Wednesday 6-8 pm, in Math 25L Helproom
- B.S. University of Geneva, Switzerland, 1998
M.A. Duke University, 2000
- Research Interests: Probability Theory: Random Walks, Brownian Motion, and the Stochastic Loewner Evolution.
The asymptotic behavior (as epsilon goes to 0) of the number of holes of area larger than epsilon made by complex Brownian motion in a unit time interval is well known. Mandelbrot suggested that the behavior of the number of "large" holes made by 2d simple random walk is the same, but that the exponent is different for holes at a "small" scale. I am investigating on this question.
I am also currently trying to show a relationship between Laplacian Random Walk (LRW) and the Schramm-Loewner Evolution (SLE). A wild conjecture is that every SLE(k) is the scaling limit of LRW(a), where a=(6-k)/2k.