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
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Colouring powers of cycles from random lists (with
Michael Krivelevich ), European J. of Combinatorics 25, 961-968, 2004.
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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