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

I am teaching a course on zoom, open to everyone, on the topic “**Laplacian growth**“

For a detailed syllabus and links, see https://bimsa.net:10000/activity/lapgro/

- Yuval Peres Presentations [Last updated June, 2022]
- Yuval Peres Youtube Channel [Last updated June, 2022]
- Yuval Peres- Videos and presentations at MSRI
- Yuval Peres Books (with selected open problems)
- Photos of Mathematicians and conferences
- Publications from 2019 Research publications until 2019. Publications on researchgate.
- Papers in Google Scholar, MathSciNet, DBLP, and arXiv
- PNAS profile and NAS bio
- My LinkedIn profile, my Amazon author page and Math genealogy
- Recently, I have been answering many questions on Mathoverflow and Mathematics Stack exchange. Here is my favorite answer.
- Web page of a course on Markov chain mixing

** Expositions and Riddles: **Discussions of problems and riddles in probability, analysis, and theoretical computer science (Last update: * Spread of a contagion in a heterogeneous population – Linear algebra tutorial, Aug 2020*).

**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.
- Fractals in Probability and Analysis, by Christopher Bishop and Yuval Peres. Cambridge University Press, 2017
- Brownian motion, by Peter Mörters and Yuval Peres. Cambridge University Press, 2010.
- 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.

- Lewicka, Marta, and Yuval Peres. “The Robin mean value equation I: A random walk approach to the third boundary value problem.” Potential Analysis: 1-32 (2022).
- Lewicka, M. and Peres, Y. The Robin mean value equation II: asymptotic Hölder regularity. Potential Analysis, pp.1-35. (2022).
- Gordon, Peter V., Fedor Nazarov, and Yuval Peres. “A basic homogenization problem for the p-Laplacian in R^d perforated along a sphere: L^{infinity} estimates.” arXiv preprint (2022).
- Elboim, Dor, Yuval Peres, and Ron Peretz. “The Asynchronous DeGroot Dynamics.” arXiv preprint (2022).
- A Ben-Hamou, Y Peres Cutoff for permuted Markov chains Annales de l’Institut Henri Poincare (B) Probabilites et statistiques 59 (1) pp. 230-243
- Nachmias, Asaf; Peres, Yuval The local limit of uniform spanning trees. Probab. Theory Related Fields 182 (2022), no. 3-4, 1133–1161.
- Bosi, Gianluca; Hu, Yiping; Peres, Yuval; Recurrence and windings of two revolving random walks. Electron. J. Probab. 27 (2022)
- Chiclana, Rafael; Peres, Yuval; No cutoff in spherically symmetric trees. Electron. Commun. Probab. 27 (2022), Paper No. 27, 11 pp.
- Holden, Nina; Peres, Yuval; Zhai, Alex Gravitational allocation for uniform points on the sphere. Ann. Probab. 49 (2021), no. 1, 287–321.
- Lyons, Russell; Peres, Yuval Poisson boundaries of lamplighter groups: proof of the Kaimanovich-Vershik conjecture. J. Eur. Math. Soc. (JEMS) 23 (2021), no. 4, 1133–1160.
- Peres, Yuval. Noise stability of weighted majority. In and out of equilibrium 3. Celebrating Vladas Sidoravicius, 677–682, Progress Probab.

77, Birkhäuser/Springer (2021). - Stabilizing a system with an unbounded random gain using only finitely many bits. Kostina, Victoria; Peres, Yuval; Ranade, Gireeja; Sellke, Mark.
*IEEE Trans. Inform. Theory*67 (2021), no. 4, 2554–2561 - Communication cost of consensus for nodes with limited memory. (
*Proceedings of the National Academy of Sciences*,*117*(11), (2020) 5624-5630. - Lyons, Russell; Peres, Yuval; Sun, Xin; Zheng, Tianyi Occupation measure of random walks and wired spanning forests in balls of Cayley graphs. Ann. Fac. Sci. Toulouse Math. (6) 29 (2020), no. 1, 97–109.
- Peres, Yuval; Sousi, Perla; Steif, Jeffrey E. Mixing time for random walk on supercritical dynamical percolation. Probab. Theory Related Fields 176 (2020), no. 3-4 809–849.
- Angel, Omer; Mehrabian, Abbas; Peres, Yuval The string of diamonds is nearly tight for rumour spreading. Combin. Probab. Comput. 29 (2020), no. 2, 190–199.
- Holroyd, Alexander E.; Martin, James B.; Peres, Yuval Stable matchings in high dimensions via the Poisson-weighted infinite tree. Ann. Inst. Henri Poincaré Probab. Stat. 56 (2020), no. 2, 826–846.
- Peres, Yuval; Zheng, Tianyi On groups, slow heat kernel decay yields Liouville property and sharp entropy bounds. Int. Math. Res. Not. IMRN 2020, no. 3, 722–750.
- Peres, Yuval; Tanaka, Ryokichi; Zhai, Alex Cutoff for product replacement on finite groups. Probab. Theory Related Fields 177 (2020), no. 3-4, 823–853.
- Brandão, Fernando G. S. L.; Harrow, Aram W.; Lee, James R.; Peres, Yuval Adversarial hypothesis testing and a quantum Stein’s lemma for restricted measurements. IEEE Trans. Inform. Theory 66 (2020), no. 8, 5037–5054.
- Lewicka, Marta; Peres, Yuval Which domains have two-sided supporting unit spheres at every boundary point? Expo. Math. 38 (2020), no. 4, 548–558.
- Analyticity for rapidly determined properties of Poisson Galton–Watson trees. (Yuval Peres and Andrew Swan).
*Electronic Communications in Probability*25 (2020). - Duminil-Copin, Hugo; Kesten, Harry; Nazarov, Fedor; Peres, Yuval; Sidoravicius, Vladas On the number of maximal paths in directed last-passage percolation. Ann. Probab. 48 (2020), no. 5, 2176–2188.
- Peres, Yuval; Rácz, Miklós Z.; Sly, Allan; Stuhl, Izabella How fragile are information cascades? Ann. Appl. Probab. 30 (2020), no. 6, 2796–2814
- Perfect Bayesian equilibria in repeated sales. (N.R. Devanur, Y. Peres, and B. Sivan). Games and Economic Behavior 118 (2019), 570–588.
- 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).
- Multiplayer bandit learning, from competition to cooperation. (Simina Branzei and Yuval Peres). COLT 2021: 679-723
- Comparing mixing times on sparse random graphs. (Anna Ben-Hamou, Eyal Lubetzky, and Yuval Peres). Ann. Inst. Henri Poincaré Probab. Stat. 55, no. 2, 1116 – 1130, 2019.
- 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, no. 1-2, 605 - 650, 2019.
- How round are the complementary components of planar Brownian motion?. ( Ann). Inst. Henri Poincaré Probab. Stat. 55, no 2, 882 – 908, 2019.
- Random walks on graphs: new bounds on hitting, meeting, coalescing and returning. ( , Proceedings of the Sixteenth Workshop on Analytic Algorithmics and Combinatorics (ANALCO) 119 – 126 SIAM, Philadelphia, PA 2019.
- The component graph of the uniform spanning forest: transitions in dimensions 9,10,11,…. (Tom Hutchcroft and Yuval Peres).
*Probab. Theory Related Fiel**d**s*175, no. 1-2, 141–208, 2019. - When multiplicative noise stymies control. (Jian Ding, Yuval Peres, Gireeja Ranade, and Alex Zhai).
*Ann. Appl. Probab.*29, no. 4, 1963–1992, 2019. - Online learning with an almost perfect expert. (Simina Branzei and Yuval Peres). PNAS , 2019.
- Mixing time estimation in reversible Markov chains from a single sample path. (Hsu, Daniel; Kontorovich, Aryeh; Levin, David A.; Peres, Yuval; Szepesvári, Csaba; Wolfer, Geoffrey).
*Ann. Appl. Probab.*29, no. 4, 2439–2480, 2019.

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

- 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.
- 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.
- 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.
- Profile in IMS Bulletin.