Asaf Nachmias' Home Page

I am a pure math instructor at MIT. Previously, I was a post-doc research at the theory group of Microsoft research, Redmond WA. I obtained my Ph.D. in mathematics at U.C. Berkeley under the supervision of Prof. Yuval Peres . My research interests are probability theory and statistical physics. I focus on percolation, random walks and mixing time of Markov chains.

Seminars

This year I am co-organizing the MIT probability seminar , and our reading seminar in probability, focusing on the recent development in 2D statistical physics. Check it out!

Curriculum Vitae

pdf

Teaching

Math 18.022 , calculus of several variables, Fall 2010.

Papers

Colouring powers of cycles from random lists (with Michael Krivelevich ), European J. of Combinatorics 25, 961-968, 2004.
Colouring complete bipartite graphs from random lists (with Michael Krivelevich ), Random Structures and Algorithms 29, no. 4, 436-449, 2006.
The critical random graph, with martingales. (with Yuval Peres ), Israel Journal of Math, 176, 29-43, 2010.
Component sizes of the random graph outside the scaling window (with Yuval Peres ), Latin American Journal of Probability and Mathematical Statistics (ALEA), 3, 133-142, 2007.
Critical random graphs: diameter and mixing time (with Yuval Peres ), Annals of Probability, 36, no. 4, 1267-1286, 2008.
Critical percolation on random regular graphs (with Yuval Peres ), Random Structures and Algorithms, 36, no. 2, 111-148, 2010.
Mixing time power laws at criticality , (with Yun Long and Yuval Peres ), Proc. of the 48th IEEE FOCS, 2007.
Mean-field conditions for percolation on finite graphs , Geometric and Functional Analysis (GAFA) , 19, 1171-1194, 2009.
Testing the expansion of a graph (with Asaf Shapira) , Information and Computation, 208, no. 4, 309-314, 2010.
The Alexander-Orbach conjecture holds in high dimensions (with Gady Kozma ), Inventiones Mathematicae, 178, no. 3, 635--654, 2009.
Is the critical percolation probability local? (with Itai Benjamini and Yuval Peres), Probability Theory and Related Fields, 149, no. 1-2, 261-269, 2011.
A note about critical percolation on finite graphs (with Gady Kozma ), Journal of Theoretical Probability, to appear.
Arm exponents in high dimensional percolation (with Gady Kozma ), Journal of the American Mathematical Society, 24, 375-409, 2011.
The evolution of the cover time (with Martin Barlow , Jian Ding and Yuval Peres), Combinatorics, Probability and Computing, to appear.
Non-concentration of return times, (with Ori Gurel-Gurevich), submitted .
A power law of order 1/4 for critical mean-field Swendsen-Wang dynamics , (with Yun Long, Weiyang Ning and Yuval Peres), submitted .

Contact information

Email: <my username>@math.mit.edu

Department of Mathematics,
Massachusetts Institute of Technology,
77 Massachusetts Avenue,
Cambridge, MA 02139