Ron Peled's Home Page

Grand Canyon, October 2005.

I'm a fourth year Ph.d. candidate in the Statistics Department at UC Berkeley . I'm doing research in Probability theory under the supervision of Prof. Steve Evans and Prof. Yuval Peres . I am interested in all areas of probability theory, continuous and discrete.
I am graduating this year and will start a new position in September as a Courant Instructor / PIRE Fellow at the Courant Institute in New-York.
Before coming to Berkeley I did a master's degree in mathematics at Tel-Aviv university under the supervision of Prof. Boris Tsirelson.
I did my undergraduate studies in mathematics at the Open University of Israel.

Papers

Gravitational allocation to Poisson points. Joint with Sourav Chatterjee, Yuval Peres and Dan Romik. To Appear in Annals of Mathematics. A slideshow is available.
Brownian motion on time scales, basic hypergeometric functions, and some continued fractions of Ramanujan. Joint with Shankar Bhamidi, Steve Evans and Peter Ralph. To Appear in Probability and Statistics: Essays in Honor of David A. Freedman, IMS Collections, Vol. 2.
Monotonicity of complexity of the Erdös-Rényi giant component. Joint with Russell Lyons and Oded Schramm. To Appear in Combinatorics, Probability and Computing.
The Maximal Probability that k-wise Independent Bits are All 1 . Joint with Ariel Yadin and Amir Yehudayoff. Preprint.
On the rough isometry of 1D Poisson processes. Submitted.
On k-wise independent events and percolation. Joint with Itai Benjamini and Ori-Gurel Gurevich. In preparation. An extended abstract and slideshow are available.
More bounds for gravitational allocation to Poisson points. Joint with Sourav Chatterjee, Yuval Peres and Dan Romik. In preparation.
Restoring topology from shifts. My master's thesis under Prof. Boris Tsirelson. Preprint.

A mathematical gallery

Below are pictures from some of the projects that I have worked on. Click on the picture for more information and related pictures.

Gradient flow / gravitational allocation (pictures courtesy of Manjunath Krishnapur) Pictures for the 2D model of zeros of the Gaussian entire function. On the left is the allocation and on the right its potential function.	K-wise independent percolation
Rough isometry of 1D percolations	Brownian motion on a geometric state space and on the Cantor set (pictures courtesy of Peter Ralph)

Teaching

Spring 2006: Stat 2 (Introduction to Statistics).
Fall 2005: Stat 134 (Concepts of Probability).
I was also a teaching assistant at Tel-Aviv university during the years 2002-2004 in the courses: Linear algebra, Calculus and ordinary differential equations for engineers.