Contents: Expositions and Riddles / Selected ResearchBooks & Lec. Notes / Lecture Videos / Students / Post Docs. / Selected Papers


 (New) Expositions and Riddles: Discussions of problems and riddles in probability, analysis, and theoretical computer science (Last updated: May 2019).

Selected Research: (click on pictures for more information)

 

Rotor-Router Model Gaussian Analytic Functions Stable Marriage of
Poisson & Lebesgue
Random Walks

Publications until 2011.

Books and Lecture Notes:

Amazon page with a collection of my books. 

Lecture Videos:

Former Ph.D. Students:

  • Elchanan Mossel (PhD 2000), Professor, MIT.  
  • David Levin (PhD 1999), Associate Professor, University of Oregon.
  • Balint Virag (PhD 2000), Professor, University of Toronto.
  • Noam Berger (PhD 2003), Professor, University of Munich and Hebrew University.
  • Nathaniel Harvey (PhD 2003). At Jet Propulsion Lab.
  • Serban Nacu (PhD 2004). At Knight Capital.
  • Alan M. Hammond (PhD 2005), Associate Professor, UC Berkeley.
  • Gabor Pete (PhD 2006), Associate Professor, Budapest University of Technology and Economics.
  • Manjunath Krishnapur (PhD 2006), Associate Professor, Indian Institute of Science, Bangalore.
  • Ben Hough (PhD 2006), at HBK.
  • Lionel Levine (PhD 2007), Associate Professor, Cornell University.
  • Asaf Nachmias (PhD 2008), Professor, Tel Aviv University.
  • Ron Peled (PhD 2008) (joint with Steve Evans), Professor, Tel Aviv University.
  • Yun Long (PhD 2009), at Bloomberg.
  • Stephanie Somersille (PhD 2009), Former postdoc at UT Austin.
  • Jian Ding (PhD 2011), Associate Professor, University of Pennsylvania.
  • Tonći Antunović (PhD 2012), Former postdoc at UCLA.
  • Elisa Celis (PhD 2012) (joint with Anna Karlin), Assistant Professor at Yale.
  • Subhroshekhar Ghosh (PhD 2013), Assistant Professor, National University of Singapore.
  • Weiyang Ning (PhD 2013).
  • Alex Zhai (PhD 2018) (joint with Amir Dembo).

Postdoctoral scholars mentored:

  • Ben Morris, NSF Postdoc 2001-2003. Professor, UC Davis.
  • Elchanan Mossel, Miller postdoctoral fellow, 2002-2003. Professor, MIT.
  • Alexander Holroyd, CPAM postdoc 2002-2003, Former senior researcher at Microsoft Research.
  • David Revelle, NSF postdoc 2002-2005.
  • Scott Sheffield, NSF postdoc 2004-2005, Professor, MIT.
  • Dan Romik, MSRI and NSF-FRG postdoc 2005-2006, Professor, UC Davis.

Other links:

Selected Papers:

  1. Cover times, blanket times, and majorizing measures . (J. Ding, J. Lee, Y. Peres). STOC 2011 and Ann. Math. 175 (2012) 1409-1471.
  2. Anatomy of a young giant component in the random graph . (J. Ding, J.H. Kim, E. Lubetzky, Y. Peres ).   Random Structures & Algorithms 38 (2011).
  3. Gravitational allocation to Poisson points . (S. Chatterjee, R. Peled, Y. Peres, D. Romik). Ann. Math. 172 (2010) 617-671.
  4. Tug-of-war and the infinity Laplacian . (Y. Peres, O. Schramm, S. Sheffield, D.B. Wilson ). J. Amer. Math. Society 22(1) (2009) 167-210.
  5. 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.
  6. 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.
  7. Entropy of Convolutions on the Circle. (E. Lindenstrauss, D. Meiri and Y. Peres) Ann. Math. 149 (1999), 871–904.
  8. Zeros of the i.i.d. Gaussian power series: a conformally invariant determinantal process. (Y. Peres and B. Vir�g). Acta Math. 194, 1–35.
  9. 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.
  10. Smoothness of projections, Bernoulli convolutions and the dimension of exceptions. (Y. Peres and W. Schlag.)Duke Math. J. 102 (2000), 193–251. 
  11. Intersection-equivalence of Brownian paths and certain branching processes (Y. Peres). Comm. Math. Phys. 177 (1996), 417–434.
  12. Broadcasting on trees and the Ising model. (W. Evans, C. Kenyon, Y. Peres and L. Schulman).  Ann. Appl. Probab. 10, (2000), 410–433.  
  13. 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.
  14. 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.