Contents: Selected Research / Lectures / Books & Lec. Notes / Talks / Students / Post Docs. / Selected Papers / Coauthors / Contact Information


Selected Research:  (click on pictures for more information)

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

Lectures:

Books and Lecture Notes:

  • Brownian motion by Peter M�rters and Yuval Peres. An errata page for this book is here.
  • Markov chains and mixing times by David A. Levin, Yuval Peres and Elizabeth L. Wilmer. An errata page for this book is here.
  • A book on “Zeros of Gaussian Analytic Functions and Determinantal Point Processes” by Ben J. Hough, Manjunath Krishnapur, Balint Virag and Yuval Peres (published by the AMS in 2010) Available here.
  • Game Theory Alive , by Anna Karlin and Yuval Peres, to be published by the American Mathematical Society (2016).
  • DRAFT Lecture notes for summer school at UBC on Mixing for Markov chains and spin systems.
  • Lecture notes on Brownian motion, edited by B�lint Vir�g  and Elchanan Mossel. From a graduate course given at the University of California, Berkeley in the spring semester, (1998). 1. (postscript file 861 KB) . 2. (PDF file 554 KB).
  • Probability on Trees: An Introductory Climb. Notes from the Saint Flour Summer School, July 1997. Prepared with Dimitris Gatzouras and David Levin. Version of March 10, 1999. The notes have appeared in Springer Lecture notes in Math 1717, (1999), pp. 193-280. 1. (postscript file 1.7 MB) . 2. (gzipped postscript file 380 KB).
  • Probability on Trees and Networks by Russell Lyons with Yuval Peres A book in progress, web version available here.
  • Notes from a course on probability on trees and networks, Berkeley, Fall 2004.  Edited by Asaf Nachmias.  (pdf file 317 KB).
  • Notes from a graduate course in probability, Berkeley, Spring 2002.  Available here.

Talks:

Students:

Former Ph.D. Students:

  • Elchanan Mossel (PhD 2000), Professor, Statistics & CS Dept UC Berkeley. Thesis:  Problems in Particle systems and Random Walks.  
  • David Levin (PhD 1999), Associate Professor at the University of Oregon.  Thesis:  Phase Transitions in Probability: Percolation and Hidden Markov Models.
  • B�lint Vir�g (PhD 2000) , Associate Proffessor at the University of Toronto.  Thesis:  Random Walk and Geometry on Graphs of Exponential Growth. 
  • Ariel Scolnicov (MSC 2001), Checkpoint.  Thesis:  Critical percolation on certain nonunimodular graphs.
  • Noam Berger (PhD 2003), Assistant Professor at Hebrew U. of Jerusalem   Thesis:  Random Walk on Percolation Clusters.
  • Nathaniel Harvey (PhD 2003).  At Jet Propulsion Lab. Thesis:  Finitary Coding.
  • Serban Nacu (PhD 2004), at Knight Captital.  Thesis:  On the Simulation of Certain Random Systems.
  • Alan M. Hammond (PhD 2005), Academic Staff at Oxford.  Thesis:  Two Models of Probability Theory: Brownian Fluctuations and a Kinetic Limit.
  • G�bor Pete (PhD 2006), Coxeter Assistant Professor at U. Toronto, will be an Assistant Professor at Technical University Budapest .  Thesis:  Dependent Percolation, Critical Exponents, Anchored Isoperimetry and Random Walks.
  • Manjunath Krishnapur (PhD 2006), Assistant Professor at Indian Institute of Science, Bangalore.   Thesis:  Zeros of Random Analytic Functions.
  • Ben Hough (PhD 2006), at HBK.   Thesis:  Asymptotic Results for Zeros of Diffusing Gaussian Analytic Functions.
  • Lionel Levine (PhD 2007), Moore instructor at MIT, will be Assistant Professor at Cornell U.   Thesis:  Limit Theorems for Internal Aggregation Models.
  • Asaf Nachmias (PhD 2008), Moore instructor at MIT, will be Assistant Professor at UBC.   Thesis:  Critical Percolation on Finite Graphs .
  • Ron Peled (PhD 2008) (joint with Steve Evans), Assistant Professor at Tel Aviv U.   Thesis:  Global Irregularities for Poisson Processes – Gravitational Allocation and Rough Isometries .
  • Yun Long (PhD 2009), at Bloomberg.   Thesis:  Mixing Time of the Swendsen-Wang Dynamics on the Complete Graph and Trees.
  • Stephanie Somersille (PhD 2009), postdoc at UT Austin.   Thesis:  Biased Tug-of-War, The Biased Infinity Laplacian and Comparison with Exponential Cones.
  • Jian Ding (PhD 2011), Assistant Professor at U. Chicago from Sep 2012.
  • Tonći Antunović (PhD 2012), postdoc at UCLA.
  • Subhroshekhar Ghosh (PhD 2013), postdoc at Princeton.
  • Weiyang Ning (PhD 2013).
  • Elisa Celis (PhD 2012) (joint with Anna Karlin), at Xerox.

Postdoctoral scholars mentored:

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