**Contents: Expositions and Riddles /**** Selected Research / Books & Lec. Notes / Recent Papers / Lecture Videos / Students / Post Docs. / Selected Papers**

- Research publications until 2019.
- Papers in Google Scholar, MathSciNet, DBLP, and arXiv
- PNAS profile and NAS bio
- MathOverflow, LinkedIn, and Math geneology
- My favorite inequality is the Varopoulos-Carne inequality. See exposition on Terry Tao’s blog and section 13.2 in the book with R. Lyons.

** (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 |

Amazon page with a collection of my books.

- Probability on Trees and Networks, by Russell Lyons and Yuval Peres. Cambridge University Press, 2016.
- Markov chains and mixing times, by David A. Levin and Yuval Peres, with contributions by Elizabeth L. Wilmer. American Mathematical Society, 2017 (errata).
- Game Theory Alive, by Anna Karlin and Yuval Peres. American Mathematical Society, 2017 (pdf).
- Fractals in Probability and Analysis, by Christopher Bishop and Yuval Peres. Cambridge University Press, 2017 (pdf)
- Brownian motion, by Peter Mörters and Yuval Peres. Cambridge University Press, 2010 (errata).
- Zeros of Gaussian Analytic Functions and Determinantal Point Processes, by Ben J. Hough, Manjunath Krishnapur, Balint Virag and Yuval Peres. American Mathematical Society, 2010.
- Probability on Trees: An Introductory Climb. Saint Flour Summer School, 1997. Prepared with Dimitris Gatzouras and David Levin. In Springer Lecture notes in Math 1717, (1999), pp. 193-280.

- The Robin mean value equation II: Asymptotic Holder regularity. (M. Lewicka and Y. Peres), submitted (2019).
- The Robin mean value equation I: A random walk approach to the third boundary value problem. (M. Lewicka and Y. Peres), submitted (2019).
- Comparing mixing times on sparse random graphs. (Anna Ben-Hamou, Eyal Lubetzky, and Yuval Peres). Ann. Inst. Henri Poincaré Probab. Stat. 55 2019, no. 2, 1116 – 1130.
- Cut-off for lamplighter chains on tori: dimension interpolation and phase transition. (Amir Dembo, Jian Ding, Jason Miller, and Yuval Peres). Probab. Theory Related Fields 173, 2019, no. 1-2, 605 - 650

Research publications until 2019 on the American Institute of Math website. Publications until 2011 on Bibserver.

- Graphs and Randomness: Part 1 and Part 2, IMPA, Brazil, 2018.
- Occupation measure of random walk in balls of Cayley graphs, IAS, Israel, 2018.
- Public lecture on Visual Mathematics, IMS, Singapore, 2018.
- Self-interacting walks and uniform spanning forests, CIRM, Paris, 2017.
- Breaking barriers in probability, IHES, Paris, 2016.
- Technion course on Markov chains mixing: Part 1, Part 2, Part 3, and Part 4.

- 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.

- Cover times, blanket times, and majorizing measures . (J. Ding, J. Lee, Y. Peres).
*STOC 2011*and*Ann. Math.***175**(2012) 1409-1471. - Anatomy of a young giant component in the random graph . (J. Ding, J.H. Kim, E. Lubetzky, Y. Peres ).
*Random Structures & Algorithms***38**(2011). - Gravitational allocation to Poisson points . (S. Chatterjee, R. Peled, Y. Peres, D. Romik).
*Ann. Math.***172**(2010) 617-671. - 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. - 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. - 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. - Entropy of Convolutions on the Circle. (E. Lindenstrauss, D. Meiri and Y. Peres)
*Ann. Math.***149**(1999), 871–904. - Zeros of the i.i.d. Gaussian power series: a conformally invariant determinantal process. (Y. Peres and B. Virag).
*Acta Math.***194**, 1–35. - 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. - Smoothness of projections, Bernoulli convolutions and the dimension of exceptions. (Y. Peres and W. Schlag.)
*Duke Math. J.***102**(2000), 193–251. - Intersection-equivalence of Brownian paths and certain branching processes (Y. Peres). Comm. Math. Phys.
**177**(1996), 417–434. - Broadcasting on trees and the Ising model. (W. Evans, C. Kenyon, Y. Peres and L. Schulman)
*. Ann. Appl. Probab.***10**, (2000), 410–433. - 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. - Rigorous location of phase transitions in hard optimization problems. (D. Achlioptas, A. Naor and Y. Peres).
*Nature***435**, (2005), 759–764.

- An article on the David P. Robbins Prize. See also exposition here.
- MSRI program on Probability, Algorithms and Statistical Physics.
- Discussion in Terry Tao’s blog.
- IMS Bulletin.