Publications

Books
  1. Large Deviations for Random Graphs. (Lecture notes for the 2015 Saint-Flour Summer School.) Springer Lecture Notes in Mathematics. Springer, Berlin-Heidelberg, 2017.
  2. Superconcentration and Related Topics. Springer Monographs in Mathematics. Springer, Cham, 2014.

Recent preprints
  1. Univariate-Guided Sparse Regression. (with Trevor Hastie and Robert Tibshirani)
  2. On the stability of solutions to random optimization problems under small perturbations. (with Souvik Ray)
  3. Neural Networks Generalize on Low Complexity Data. (with Timothy Sudijono)
  4. A Vershik-Kerov theorem for wreath products. (with Persi Diaconis)
  5. A scaling limit of SU(2) lattice Yang-Mills-Higgs theory.
  6. Spin glass phase at zero temperature in the Edwards-Anderson model.
  7. Convergence of gradient descent for deep neural networks.

Published or accepted papers
  1. Liouville Theory: An Introduction to Rigorous Approaches. (with Edward Witten) To appear in J. High Energy Phys.
  2. Spectral gap of nonreversible Markov chains. To appear in Ann. App. Probab.
  3. Estimating large causal polytrees from small samples. (with Mathukumalli Vidyasagar) To appear in Indian J. Pure Appl. Math., special issue in honor of K. R. Parthasarathy.
  4. An invariance principle for the 1D KPZ equation. (with Arka Adhikari) Ann. Probab., 52 No. 6, 2019-2050, 2024.
  5. A survey of some recent developments in measures of association. In Probability and Stochastic Processes (Volume in Honour of Rajeeva L. Karandikar). Athreya, S., Bhatt, A. G., Rao, B. V. (eds). Springer, Singapore, 2024.
  6. Enumerative Theory for the Tsetlin Library. (with Persi Diaconis and Gene Kim) J. Algebra. 655, 139-162, 2024.
  7. Features of a spin glass in the random field Ising model. Comm. Math. Phys., 405, article no. 93, 2024.
  8. A state space for 3D Euclidean Yang-Mills theories. (with Sky Cao) Comm. Math. Phys., 405, article no. 3, 2024.
  9. The Yang-Mills heat flow with random distributional initial data. (with Sky Cao) Comm. Partial Diff. Eq., 48 no. 2, 209-251, 2023.
  10. Existence of stationary ballistic deposition on the infinite lattice. Random Structures and Algorithms, 62 no. 3, 600-622, 2023.
  11. Weak convergence of directed polymers to deterministic KPZ at high temperature. Ann. de l'Inst. Henri Poincaré Probab. Stat., 59 no. 2, 774-794, 2023.
  12. Superconcentration in surface growth. Random Structures and Algorithms, 62, 304-334, 2023.
  13. Isomorphisms between random graphs. (with Persi Diaconis) J. Combin. Theory, Ser. B., 160, 144-162, 2023.
  14. A random walk on the Rado graph. (with Persi Diaconis and Laurent Miclo) In Toeplitz Operators and Random Matrices, in honor of Harold Widom. Edited by E. Basor, A. Böttcher, T. Ehrhardt, and C. A. Tracy. Springer Nature, Switzerland, 2022.
  15. Local KPZ behavior under arbitrary scaling limits. Comm. Math. Phys.. 396 no. 3, 1277-1304, 2022.
  16. Matrix completion with data-dependent missingness probabilities. (with Sohom Bhattacharya) IEEE Trans. Inf. Theory., 68 no. 10, 6762-6773, 2022.
  17. Convergence of deterministic growth models. (with Panagiotis E. Souganidis) Arch. Rational Mech. Anal., 245 no. 2, 863-898, 2022.
  18. A phase transition for repeated averages. (with Persi Diaconis, Allan Sly and Lingfu Zhang) Ann. Probab., 50 no. 1, 1-17, 2022.
  19. A new coefficient of correlation. J. Amer. Statist. Assoc., 116 no. 536, 2009-2022, 2021.
  20. A simple measure of conditional dependence. (with Mona Azadkia) Ann. Statist., 49 no. 6, 3070-3102, 2021.
  21. A probabilistic mechanism for quark confinement. Comm. Math. Phys., 385, 1007-1039, 2021.
  22. Average Gromov hyperbolicity and the Parisi ansatz. (with Leila Sloman) Adv. Math., 376, 107417, 2021.
  23. A deterministic theory of low rank matrix completion. IEEE Trans. Inf. Theory, 66 no. 12, 8046-8055, 2020.
  24. Speeding up Markov chains with deterministic jumps. (with Persi Diaconis) Probab. Theory Related Fields (special issue in honor of Harry Kesten) 178 no. 3, 1193-1214, 2020.
  25. Fluctuation lower bounds in planar random growth models. (with Erik Bates) Ann. de l'Inst. Henri Poincaré Probab. Stat., 56 no. 4, 2406-2427, 2020.
  26. Localization in Gaussian disordered systems at low temperature. (with Erik Bates) Ann. Probab., 48 no. 6, 2755-2806, 2020.
  27. Wilson loops in Ising lattice gauge theory. Comm. Math. Phys., 377, 307-340, 2020.
  28. Constructing a solution of the (2 + 1)-dimensional KPZ equation. (with Alexander Dunlap) Ann. Probab., 48 no. 2, 1014-1055, 2020.
  29. The endpoint distribution of directed polymers. (with Erik Bates) Ann. Probab., 48 no. 2, 817-871, 2020.
  30. Localization in random geometric graphs with too many edges. (with Matan Harel) Ann. Probab., 48 no. 2, 574-621, 2020.
  31. Rigidity of the three-dimensional hierarchical Coulomb gas. Probab. Theory Related Fields, 175 no. 3, 1123-1176, 2019.
  32. Proof of the path localization conjecture for directed polymers. Comm. Math. Phys., 370, 703-717, 2019.
  33. A general method for lower bounds on fluctuations of random variables. Ann. Probab., 47 no. 4, 2140-2171, 2019.
  34. Yang-Mills for probabilists. In Probability and Analysis in Interacting Physical Systems: In honor of S. R. S. Varadhan, pp. 1-16, Springer, Berlin, 2019.
  35. Central limit theorem for the free energy of the random field Ising model. J. Stat. Phys., 175, 185-202, 2019.
  36. Rigorous solution of strongly coupled SO(N) lattice gauge theory in the large N limit. Comm. Math. Phys., 366, 203-268, 2019.
  37. On the decay of correlations in the random field Ising model. Comm. Math. Phys., 362 no. 1, 253-267, 2018.
  38. Arbitrarily small perturbations of Dirichlet Laplacians are quantum unique ergodic. (with Jeffrey Galkowski) J. Spectr. Theory., 8 no. 3, 909-947, 2018.
  39. The sample size required in importance sampling. (with Persi Diaconis) Ann. App. Probab., 28 no. 2, 1099-1135, 2018.
  40. Discussion of the paper on "Concentration for (regularized) empirical risk minimization" by Sara van de Geer and Martin Wainwright. Sankhya A, 79 no. 2, 208-211, 2017.
  41. A central limit theorem for a new statistic on permutations. (with Persi Diaconis) Indian J. Pure App. Math., (special issue in honor of Prof. B. V. Rao) 48 no. 4, 561-573, 2017.
  42. A note about the uniform distribution on the intersection of a simplex and a sphere. J. Topol. Anal., 9 no. 4, 717-738, 2017.
  43. Minimal spanning trees and Stein's method. (with Sanchayan Sen) Ann. App. Probab., 27 no. 3, 1588-1645, 2017.
  44. The leading term of the Yang-Mills free energy. J. Funct. Anal., 271, 2944-3005, 2016.
  45. An introduction to large deviations for random graphs. Bull. Amer. Math. Soc., 53 no. 4, 617-642, 2016.
  46. Nonlinear large deviations. (with Amir Dembo) Adv. Math., 299, 396-450, 2016.
  47. Absence of replica symmetry breaking in the random field Ising model. Comm. Math. Phys., 337 no. 1, 93-102, 2015.
  48. Matrix estimation by Universal Singular Value Thresholding. Ann. Statist., 43 no. 1, 177-214, 2015.
  49. A short survey of Stein's method. Proceedings of ICM 2014, Vol IV, 1-24, 2014.
  50. A new perspective on least squares under convex constraint. Ann. Statist., 42 no. 6, 2340-2381, 2014.
  51. Invariant measures and the soliton resolution conjecture. Comm. Pure Appl. Math., 67 no. 11, 1737-1842, 2014.
  52. Fluctuations of the Bose-Einstein condensate. (with Persi Diaconis) J. Phys. A: Math. Theor., 47, 085201 (23pp), 2014.
  53. Estimating and Understanding Exponential Random Graph Models. (with Persi Diaconis) Ann. Statist., 41 no. 5, 2428-2461, 2013.
  54. Central limit theorem for first-passage percolation time across thin cylinders. (with Partha S. Dey) Probab. Theory Related Fields, 156 nos. 3-4, 613--663, 2013.
  55. Random Overlap Structures: Properties and Applications to Spin Glasses. (with Louis-Pierre Arguin) Probab. Theory Related Fields, 156 nos. 1-2, 375-413, 2013.
  56. The universal relation between scaling exponents in first-passage percolation. Ann. Math. (2), 177 no. 2, 663-697, 2013.
  57. The missing log in large deviations for triangle counts. Random Structures and Algorithms, 40 no. 4, 437-451, 2012.
  58. Probabilistic methods for discrete nonlinear Schrödinger equations. (with Kay Kirkpatrick) Comm. Pure Appl. Math., 65 no. 5, 727-757, 2012.
  59. A new approach to strong embeddings. Probab. Theory Related Fields, 152, 231-264, 2012.
  60. Large deviations for random matrices. (with S. R. S. Varadhan) Comm. Stoch. Analysis, 6 no. 1, 1-13, 2012.
  61. Random multiplicative functions in short intervals. (with Kannan Soundararajan) Int. Math. Res. Not., 2012 no. 3, 479-492, 2012.
  62. The large deviation principle for the Erdős-Rényi random graph. (with S. R. S. Varadhan) European J. Comb., (special issue on Homomorphisms and Limits) 32 no. 7, 1000-1017, 2011.
  63. Spectral clustering and the high-dimensional Stochastic Block Model. (with Karl Rohe and Bin Yu) Ann. Statist., 39 no. 4, 1878-1915, 2011.
  64. A combinatorial analysis of interacting diffusions. (with Soumik Pal) J. Theoret. Probab., 24, 939-968, 2011.
  65. Random graphs with a given degree sequence. (with Persi Diaconis and Allan Sly) Ann. App. Probab., 21 no. 4, 1400-1435, 2011.
  66. Exponential Approximation by Exchangeable Pairs and Spectral Graph Theory. (with Jason Fulman and Adrian Roellin) ALEA, 8, 1-27, 2011.
  67. Non-normal approximation by Stein's Method of Exchangeable Pairs with Application to the Curie-Weiss Model. (with Qi-Man Shao) Ann. App. Probab., 21 no. 2, 464-483, 2011.
  68. Phase Transitions in Gravitational Allocation. (with Ron Peled, Dan Romik and Yuval Peres) Geom. Funct. Anal., 20, 870-917, 2010.
  69. Applications of Stein's method for concentration inequalities. (with Partha S. Dey) Ann. Probab., 38 no. 6, 2443-2485, 2010.
  70. Spin glasses and Stein's method. Probab. Theory Related Fields., 148 nos. 3-4, 567-600, 2010.
  71. Gravitational allocation to Poisson points. (with Ron Peled, Yuval Peres and Dan Romik) Ann. Math. (2), 172 no. 1, 617-671, 2010.
  72. A phase transition behavior for Brownian motions interacting through their ranks. (with Soumik Pal) Probab. Theory Related Fields, 147, 123-159, 2010.
  73. Central Limit Theorems for the Energy Density in the Sherrington-Kirkpatrick Model. (with Nicholas Crawford) J. Statist. Phys.,, 137, 639--666, 2009.
  74. An observation about submatrices. (with Michel Ledoux) Elec. Comm. Probab., 14, 495-500, 2009.
  75. Consistent Estimates of Deformed Isotropic Gaussian Random Fields on the Plane. (with Ethan Anderes) Ann. Statist., 37 no. 5A, 2324-2350, 2009.
  76. Fluctuations of eigenvalues and second order Poincaré inequalities. Probab. Theory Related Fields, 143, 1-40, 2009.
  77. Multivariate normal approximation using exchangeable pairs. (with Elizabeth Meckes) ALEA, 4, 257-283, 2008.
  78. A new method of normal approximation. Ann. Probab., 36 no. 4, 1584-1610, 2008.
  79. Estimation in spin glasses: A first step. Ann. Statist., 35 no. 5, 1931-1946, 2007.
  80. Concentration of Haar measures, with an application to random matrices. J. Funct. Anal., 245, 379-389, 2007.
  81. Stein's method for concentration inequalities. Probab. Theory Related Fields, 138, 305-321, 2007.
  82. A generalization of the Lindeberg principle. Ann. Probab., 34 no. 6, 2061-2076, 2006.
  83. Concentration inequalities with exchangeable pairs. Ph.D. thesis, Stanford University, 2005.
  84. Exchangeable pairs and Poisson approximation. (with Persi Diaconis and Elizabeth Meckes) Probab. Surv., 2, 64-106, 2005.
  85. A new method for bounding rates of convergence of empirical spectral distributions. (with Arup Bose) J. Theoret. Probab., 17 no. 4, 1003-1019, 2004.
  86. Limiting spectral distributions of large dimensional random matrices. (with Arup Bose and Sreela Gangyopadhyay) J. Indian Statist. Assoc., 41 no. 2, 221-259, 2003.

Other preprints
  1. Universality of deterministic KPZ.
  2. The 1/N expansion for SO(N) lattice gauge theory at strong coupling. (with Jafar Jafarov)
  3. High dimensional regression and matrix estimation without tuning parameters.
  4. Prediction error of cross-validated Lasso. (with Jafar Jafarov)
  5. On level sets of Gaussian fields. (with Amir Dembo and Jian Ding)
  6. Stochastic solutions of the wave equation.
  7. Assumptionless consistency of the Lasso.
  8. Properties of Uniform Doubly Stochastic Matrices (with Persi Diaconis and Allan Sly)
  9. Disorder chaos and multiple valleys in spin glasses.
  10. Chaos, concentration, and multiple valleys.
  11. The Ghirlanda-Guerra identities without averaging.
  12. A simple invariance theorem.
  13. An error bound in the Sudakov-Fernique inequality.