Grand Canyon, October 2005.

Ron Peled's Home Page

I am an associate professor in the School of Mathematical Sciences of Tel Aviv University. I am interested in all areas of Probability Theory, continuous and discrete. I am also very interested in Analysis, Combinatorics and Statistical Physics and their appearance in Probability Theory.
Previously I was a Courant Instructor / PIRE Fellow at the Courant Institute of Mathematical Sciences in New York. I spent the Fall 2008 semester as a participant in the special semester on "Interacting Particle Systems, Statistical Mechanics and Probability Theory" held at the Institut Henri Poincare.
I completed my Ph.D. in 2008 at the Statistics Department of UC Berkeley. My supervisors were Prof. Steve Evans and Prof. Yuval Peres. 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.


Support from the Israeli Science Foundation grants 1048/11 and 861/15, the Marie Skłodowska-Curie Actions International Reintegration Grant SPTRF and the ERC Starting Grant LocalOrder is gratefully acknowledged.

Lecture Notes and Videos of Talks


A Mathematical Gallery

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

Uniformly sampled homomorphism and Lipschitz functions in 2 and 3 dimensions
Left column: homomorphism and Lipschitz functions on a 100 x 100 square with zero boundary values
Right column: middle slice of homomorphism and Lipschitz functions on a 100 x 100 x 100 cube with zero boundary values

Top: the outermost level sets separating zeros and ones of a uniformly sampled homomorphism on a 40 x 40 and 300 x 300 squares with zero boundary values (pictures produced with the help of Steven M. Heilman)
Bottom: The shift transformation applied to the level set of a homomorphism function. This transformation is a major tool in the analysis of homomorphism functions in high dimensions

Gradient Flow / Gravitational Allocation (pictures based on code by Manjunath Krishnapur)
First row: Allocation to the zeros of the planar, hyperbolic and spherical canonical Gaussian Analytic Functions (all cells have equal areas!)
Second row: The potential for the allocations to the planar and hyperbolic Gaussian Analytic Functions.

K-wise independent percolation

4 coloring of Poisson-Voronoi map.

Rough isometry of 1D percolations

Brownian motion on a geometric state space and on the Cantor set
(pictures courtesy of Peter Ralph)




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