Yuval Peres

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

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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/

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• 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

Books and Lecture Notes:

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.

Recent Papers (2019-2022):

1. 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).
2. Lewicka, M. and Peres, Y. The Robin mean value equation II: asymptotic Hölder regularity. Potential Analysis, pp.1-35. (2022).
3. 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).
4. Elboim, Dor, Yuval Peres, and Ron Peretz. “The Asynchronous DeGroot Dynamics.” arXiv preprint (2022).
5. 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
6. Nachmias, Asaf; Peres, Yuval The local limit of uniform spanning trees. Probab. Theory Related Fields 182 (2022), no. 3-4, 1133–1161.
7. Bosi, Gianluca; Hu, Yiping; Peres, Yuval; Recurrence and windings of two revolving random walks. Electron. J. Probab. 27 (2022)
8. Chiclana, Rafael; Peres, Yuval; No cutoff in spherically symmetric trees. Electron. Commun. Probab. 27 (2022), Paper No. 27, 11 pp.
9. Holden, Nina; Peres, Yuval; Zhai, Alex Gravitational allocation for uniform points on the sphere. Ann. Probab. 49 (2021), no. 1, 287–321.
10. 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.
11. Peres, Yuval. Noise stability of weighted majority. In and out of equilibrium 3. Celebrating Vladas Sidoravicius, 677–682, Progress Probab.
    77, Birkhäuser/Springer (2021).
12.  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
13. Communication cost of consensus for nodes with limited memory. (Giulia Fanti, Nina Holden, Yuval Peres, and Gireeja Ranade).  Proceedings of the National Academy of Sciences, 117(11), (2020) 5624-5630.
14. 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.
15. 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.
16. 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.
17. 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. 
18. 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.
19. Peres, Yuval; Tanaka, Ryokichi; Zhai, Alex Cutoff for product replacement on finite groups. Probab. Theory Related Fields 177 (2020), no. 3-4, 823–853.
20. 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.
21. Lewicka, Marta; Peres, Yuval Which domains have two-sided supporting unit spheres at every boundary point? Expo. Math. 38 (2020), no. 4, 548–558.
22. Analyticity for rapidly determined properties of Poisson Galton–Watson trees. (Yuval Peres and Andrew Swan). Electronic Communications in Probability 25 (2020).
23. 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.
24. Peres, Yuval; Rácz, Miklós Z.; Sly, Allan; Stuhl, Izabella How fragile are information cascades? Ann. Appl. Probab. 30 (2020), no. 6, 2796–2814
25. Perfect Bayesian equilibria in repeated sales.  (N.R. Devanur, Y. Peres, and B. Sivan). Games and Economic Behavior 118 (2019), 570–588.
26. The Robin mean value equation II: Asymptotic Holder regularity. (M. Lewicka and Y. Peres), submitted (2019).
27. The Robin mean value equation I: A random walk approach to the third boundary value problem. (M. Lewicka and Y. Peres), submitted (2019).
28. Multiplayer bandit learning, from competition to cooperation. (Simina Branzei and Yuval Peres). COLT 2021: 679-723
29. 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.
30. 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.
31. How round are the complementary components of planar Brownian motion?. (Nina Holden, Şerban Nacu, Yuval Peres, and Thomas S. Salisbury Ann). Inst. Henri Poincaré Probab. Stat. 55, no 2, 882 – 908, 2019.
32. Random walks on graphs: new bounds on hitting, meeting, coalescing and returning. (Roberto Oliveira and Yuval Peres), Proceedings of the Sixteenth Workshop on Analytic Algorithmics and Combinatorics (ANALCO) 119 – 126 SIAM, Philadelphia, PA 2019.
33. The component graph of the uniform spanning forest: transitions in dimensions 9,10,11,…. (Tom Hutchcroft and Yuval Peres). Probab. Theory Related Fields 175, no. 1-2, 141–208, 2019.
34. When multiplicative noise stymies control. (Jian Ding, Yuval Peres, Gireeja Ranade, and Alex Zhai). Ann. Appl. Probab. 29, no. 4, 1963–1992, 2019.
35. Online learning with an almost perfect expert. (Simina Branzei and Yuval Peres). PNAS 116 (13) 5949-5954, 2019.
36. 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. 

Lecture Videos:

• 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.

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.
• 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.

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. Virag). 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.

Other links:

• 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.