Yuval Peres

• U.C. Berkeley probability seminar.
• U.C Berkeley probability home page.
• Papers
• Research papers on the arxiv.

  

  Rotor-Router Model

• Reviews of my papers in MathSciNet.
• Report of a Workshop on Current and Emerging Research Opportunities in Probability.

Teaching, Spring 2006:

• Problems in probability (Stat 260) , A graduate course. Tuesday and Thursday, 2-3:30 in room 332, Evans Hall.

Selected Research:  (click on pictures for more information)

Students:

Former Ph.D. Students:

• Elchanan Mossel (PhD 2000), Currently Assistant Professor, Statistics Dept UC Berkeley. Thesis:  Problems in Particle systems and Random Walks  
• David Levin (PhD 1999), Currently at the University of Oregon.  Thesis:  Phase Transitions in Probability: Percolation and Hidden Markov Models.
• Bálint Virág (PhD 2000) , Currently at the University of Toronto.  Thesis:  Random Walk and Geometry on Graphs of Exponential Growth. 
• Ariel Scolnicov (MSC 2001), currently at "Checkpoint".  Thesis:  Critical percolation on certain nonunimodular graphs.
• Noam Berger (PhD 2003), Currently at UCLA.  Thesis:  Random Walk on Percolation Clusters.
• Nathaniel Harvey (PhD 2003).  Thesis:  Finitary Coding.
• Serban Nacu (PhD 2004), Currently postdoc at Stanford.  Thesis:  On the Simulation of Certain Random Systems.
• Alan M. Hammond (PhD 2005), Currently at University of British Columbia.  Thesis:  Two Models of Probability Theory: Brownian Fluctuations and a Kinetic Limit

Current Ph.D. Students:

• Gábor Pete
• Manjunath Krishnapur
• Ben Hough
• Lionel Levine
• Asaf Nachmias
• Yun Long

Postdoctoral scholars mentored:

• Ben Morris, NSF Postdoc 2001-2003.  Starting Tenured position at UC Davis in Fall 2005.
• Elchanan Mossel, Miller postdoctoral fellow, 2002-2003.  Currently tenure-track assistant Professor, UC Berkeley Statistics.
• Alexander Holroyd, CPAM postdoc 2002-2003, currently at UBC
• David Revelle, NSF postdoc 2002-2005.
• Scott Sheffield, NSF postdoc 2004-2005.
• Dan Romik, MSRI and NSF-FRG postdoc 2005-2006.

Teaching, Fall 2005:

• Game theory (Stat 155) , an undergraduate course. Tuesday and Thursday, 2-3:30 in room 330, Evans Hall.
• Honors introduction to analysis (Math H104)

Other Links:

• Surveys and open problems. (with links to postscript files).  Updated April 2005.
• Photo with Alon Peres, May 1996.
• I am a member of the editorial board for Combinatorics, Probability & Computing and the Electronic Journal of Probability.
• Math geneology.
• MSRI program on Probability, Algorithms and Statistical Physics.
• NSF-FRG Grant #0244479: Phase Transitions in Stochastics Dynamics and Algorithms.  Click here for more information.
• NSF grant #0104073:  Spin Systems on Graphs, Critical Percolation and Scaling Limits.  Click here for more information.

Selected Papers:

1. Cover Times for Brownian Motion and Random Walks in Two Dimensions. (A. Dembo, Y. Peres, J. Rosen, and O. Zeitouni).  Ann. Math., 160 (2004)
   433--464.
2. Geometry of the uniform spanning forest: phase transitions in dimensions 4,8,12,... (I. Benjamini, H. Kesten, Y. Peres and O. Schramm.) Ann. Math., 160 (2004), 465--491.
3. Entropy of Convolutions on the Circle. (E. Lindenstrauss, D. Meiri and Y. Peres) Ann. Math. 149, (1999), 871--904.
4. Zeros of the i.i.d. Gaussian power series: a conformally invariant determinantal process. (Y. Peres and B. Virág). Acta Math.  194, (194), 1--35.
5. Thick points for planar Brownian motion and the Erdos-Taylor conjecture on random walk. (A. Dembo, Y. Peres, J. Rosen and O. Zeitouni).  Acta Math. 186 no. 2, (2001),  239--270.
6. Smoothness of projections, Bernoulli convolutions and the dimension of exceptions. (Y. Peres and W. Schlag.)Duke Math. J. 102, (2000), 193--251. 
7. Intersection-equivalence of Brownian paths and certain branching processes (Y. Peres). Comm. Math. Phys. 177 (1996), 417--434.
8. Broadcasting on trees and the Ising model. (W. Evans, C. Kenyon, Y. Peres and L. Schulman).  Ann. Appl. Probab. 10, (2000), 410--433.  
9. Glauber Dynamics on Trees and Hyperbolic Graphs. (N. Berger,  C. Kenyon, E. Mossel and Y. Peres) Probability Theory and Related Fields. 131 (2005), no.3, 311-340.  Version by C. Kenyon, E. Mossel and Y. Peres appeared in   42nd IEEE Symposium on Foundations of Computer Science (Las Vegas, NV, 2001), 568--578.
10. Rigorous location of phase transitions in hard optimization problems.  (D. Achlioptas, A. Naor and Y. Peres).  Nature 435, (2005), 759--764.

Click here for other papers available online.

Coauthors:

Dimitris Achlioptas, Noga Alon, Alano Ancona, Omer Angel, Jozsef Balogh, Itai Benjamini, Dani Berend, Noam Berger, Ron Blei, Chris Bishop, Joseph T. Chang, L. Chayes, Dayue Chen, Amir Dembo, Steven N. Evans, William Evans, Hillel Furstenberg, Nina Gantert, Dimitrios Gatzouras, Olle Haggstrom, Alan Hammond, Nate Harvey, Christopher Hoffman, Alexander E. Holroyd, J. Ben Hough, Irene Hueter, Johan Jonasson, Peter W. Jones, Claire Kenyon, Richard W. Kenyon, Harry Kesten, Davar Khoshnevisan, Yuri Kifer, Ilya Krasikov, Manjunath Krishnapur, Thomas G. Kurtz, David Levin , Lionel Levine, Elon Lindenstrauss, Russell Lyons, David Meiri, Ben Morris, Elchanan Mossel, Asaf Nachmias, Assaf Naor, Serban Nacu, Robin Pemantle , Gábor Pete, Jim Pitman, Michal Rams, David Revelle, Dan Romik, Jay Rosen, Scott Sheffield,  Wilhelm Schlag, James Schmerl, Roberto Schonmann , Oded Schramm , Leonard Schulman, Ariel Scolnicov, Jonathan W. Shapiro, Zhan Shi, Paul Shields,  Károly Simon, Alistair Sinclair, Boris Solomyak , Jeff Steif, Bálint Virág, Benjamin Weiss, David Wilson, Yimin Xiao, Marc Yor, Ofer Zeitouni