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

- A scaling limit of SU(2) lattice Yang-Mills-Higgs theory.
- Spectral gap of nonreversible Markov chains.
- Features of a spin glass in the random field Ising model.
- Spin glass phase at zero temperature in the Edwards-Anderson model.
- Estimating large causal polytrees from small samples. (with Mathukumalli Vidyasagar)
- Convergence of gradient descent for deep neural networks.

- A state space for 3D Euclidean Yang-Mills theories. (with Sky Cao) To appear in
*Comm. Math. Phys.* - A survey of some recent developments in measures of association. To appear in
*Probability and Stochastic Processes - A Volume in Honour of Rajeeva L. Karandikar.* - An invariance principle for the 1D KPZ equation. (with Arka Adhikari) To appear in
*Ann. Probab.* - Enumerative Theory for the Tsetlin Library. (with Persi Diaconis and Gene Kim) To appear in
*J. Algebra.* - 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,*2023. - The Yang-Mills heat flow with random distributional initial data. (with Sky Cao)
*Comm. Partial Diff. Eq.,***48**no. 2, 209-251, 2023. - Existence of stationary ballistic deposition on the infinite lattice.
*Random Structures and Algorithms,***62**no. 3, 600-622, 2023. - 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. - Superconcentration in surface growth.
*Random Structures and Algorithms,***62**, 304-334, 2023. - Isomorphisms between random graphs. (with Persi Diaconis)
*J. Combin. Theory, Ser. B.,***160**, 144-162, 2023. - Local KPZ behavior under arbitrary scaling limits.
*Comm. Math. Phys..***396**no. 3, 1277-1304, 2022. - Matrix completion with data-dependent missingness probabilities. (with Sohom Bhattacharya)
*IEEE Trans. Inf. Theory.,***68**no. 10, 6762-6773, 2022. - Convergence of deterministic growth models. (with Panagiotis E. Souganidis)
*Arch. Rational Mech. Anal.,***245**no. 2, 863-898, 2022. - A phase transition for repeated averages. (with Persi Diaconis, Allan Sly and Lingfu Zhang)
*Ann. Probab.,***50**no. 1, 1-17, 2022. - A new coefficient of correlation.
*J. Amer. Statist. Assoc.,***116**no. 536, 2009-2022, 2021. - A simple measure of conditional dependence. (with Mona Azadkia)
*Ann. Statist.,***49**no. 6, 3070-3102, 2021. - A probabilistic mechanism for quark confinement.
*Comm. Math. Phys.,***385**, 1007-1039, 2021. - Average Gromov hyperbolicity and the Parisi ansatz. (with Leila Sloman)
*Adv. Math.,***376**, 107417, 2021. - A deterministic theory of low rank matrix completion.
*IEEE Trans. Inf. Theory,***66**no. 12, 8046-8055, 2020. - 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. - 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. - Localization in Gaussian disordered systems at low temperature. (with Erik Bates)
*Ann. Probab.,***48**no. 6, 2755-2806, 2020. - Wilson loops in Ising lattice gauge theory.
*Comm. Math. Phys.,***377**, 307-340, 2020. - Constructing a solution of the (2 + 1)-dimensional KPZ equation. (with Alexander Dunlap)
*Ann. Probab.,***48**no. 2, 1014-1055, 2020. - The endpoint distribution of directed polymers. (with Erik Bates)
*Ann. Probab.,***48**no. 2, 817-871, 2020. - Localization in random geometric graphs with too many edges. (with Matan Harel)
*Ann. Probab.,***48**no. 2, 574-621, 2020. - Rigidity of the three-dimensional hierarchical Coulomb gas.
*Probab. Theory Related Fields,***175**no. 3, 1123-1176, 2019. - Proof of the path localization conjecture for directed polymers.
*Comm. Math. Phys.,***370**, 703-717, 2019. - A general method for lower bounds on fluctuations of random variables.
*Ann. Probab.,***47**no. 4, 2140-2171, 2019. - 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. - Central limit theorem for the free energy of the random field Ising model.
*J. Stat. Phys.,***175**, 185-202, 2019. - Rigorous solution of strongly coupled
*SO*(*N*) lattice gauge theory in the large*N*limit.*Comm. Math. Phys.,***366**, 203-268, 2019. - On the decay of correlations in the random field Ising model.
*Comm. Math. Phys.,***362**no. 1, 253-267, 2018. - Arbitrarily small perturbations of Dirichlet Laplacians are quantum unique ergodic. (with Jeffrey Galkowski)
*J. Spectr. Theory.,***8**no. 3, 909-947, 2018. - The sample size required in importance sampling. (with Persi Diaconis)
*Ann. App. Probab.,***28**no. 2, 1099-1135, 2018. - 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. - 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. - A note about the uniform distribution on the intersection of a simplex and a sphere.
*J. Topol. Anal.,***9**no. 4, 717-738, 2017. - Minimal spanning trees and Stein's method. (with Sanchayan Sen)
*Ann. App. Probab.,***27**no. 3, 1588-1645, 2017. - The leading term of the Yang-Mills free energy.
*J. Funct. Anal.,***271**, 2944-3005, 2016. -
An introduction to large deviations for random graphs.
*Bull. Amer. Math. Soc.,***53**no. 4, 617-642, 2016. - Nonlinear large deviations. (with Amir Dembo)
*Adv. Math.,***299**, 396-450, 2016. - Absence of replica symmetry breaking in the random field Ising model.
*Comm. Math. Phys.,***337**no. 1, 93-102, 2015. - Matrix estimation by Universal Singular Value Thresholding.
*Ann. Statist.,***43**no. 1, 177-214, 2015. - A short survey of Stein's method.
*Proceedings of ICM 2014,*Vol IV, 1-24, 2014. - A new perspective on least squares under convex constraint.
*Ann. Statist.,***42**no. 6, 2340-2381, 2014. - Invariant measures and the soliton resolution conjecture.
*Comm. Pure Appl. Math.,***67**no. 11, 1737-1842, 2014. - Fluctuations of the Bose-Einstein condensate. (with Persi Diaconis)
*J. Phys. A: Math. Theor.,***47**, 085201 (23pp), 2014. - Estimating and Understanding Exponential Random Graph Models. (with Persi Diaconis)
*Ann. Statist.,***41**no. 5, 2428-2461, 2013. -
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. - Random Overlap Structures: Properties and Applications to Spin Glasses. (with Louis-Pierre Arguin)
*Probab. Theory Related Fields,***156**nos. 1-2, 375-413, 2013. - The universal relation between scaling exponents in first-passage percolation.
*Ann. Math. (2),***177**no. 2, 663-697, 2013. -
The missing log in large deviations for triangle counts.
*Random Structures and Algorithms,***40**no. 4, 437-451, 2012. -
Probabilistic methods for discrete nonlinear Schrödinger equations. (with Kay Kirkpatrick)
*Comm. Pure Appl. Math.,***65**no. 5, 727-757, 2012. -
A new approach to strong embeddings.
*Probab. Theory Related Fields,***152**, 231-264, 2012. - Large deviations for random matrices. (with S. R. S. Varadhan)
*Comm. Stoch. Analysis,***6**no. 1, 1-13, 2012. - Random multiplicative functions in short intervals. (with Kannan Soundararajan)
*Int. Math. Res. Not.,***2012**no. 3, 479-492, 2012. - 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. -
Spectral clustering and the high-dimensional Stochastic Block Model. (with Karl Rohe and Bin Yu)
*Ann. Statist.,***39**no. 4, 1878-1915, 2011. - A combinatorial analysis of interacting diffusions. (with Soumik Pal)
*J. Theoret. Probab.,***24**, 939-968, 2011. -
Random graphs with a given degree sequence. (with Persi Diaconis and Allan Sly)
*Ann. App. Probab.,***21**no. 4, 1400-1435, 2011. - Exponential Approximation by Exchangeable Pairs and Spectral Graph Theory. (with Jason Fulman and Adrian Roellin)
*ALEA,***8**, 1-27, 2011. -
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. - Phase Transitions in Gravitational Allocation. (with Ron Peled, Dan Romik and Yuval Peres)
*Geom. Funct. Anal.,***20**, 870-917, 2010. - Applications of Stein's method for concentration inequalities. (with Partha S. Dey)
*Ann. Probab.,***38**no. 6, 2443-2485, 2010. -
Spin glasses and Stein's method.
*Probab. Theory Related Fields.,***148**nos. 3-4, 567-600, 2010. -
Gravitational allocation to Poisson points. (with Ron Peled, Yuval Peres and Dan Romik)
*Ann. Math. (2),***172**no. 1, 617-671, 2010. -
A phase transition behavior for Brownian motions interacting through their ranks. (with Soumik Pal)
*Probab. Theory Related Fields,***147**, 123-159, 2010. - Central Limit Theorems for the Energy Density in the Sherrington-Kirkpatrick Model. (with Nicholas Crawford)
*J. Statist. Phys.,*,**137**, 639--666, 2009. -
An observation about submatrices. (with Michel Ledoux)
*Elec. Comm. Probab.,***14**, 495-500, 2009. -
Consistent Estimates of Deformed Isotropic Gaussian Random Fields on the Plane. (with Ethan Anderes)
*Ann. Statist.,***37**no. 5A, 2324-2350, 2009. -
Fluctuations of eigenvalues and second order Poincaré inequalities.
*Probab. Theory Related Fields,***143**, 1-40, 2009. -
Multivariate normal approximation using exchangeable pairs. (with Elizabeth Meckes)
*ALEA,***4**, 257-283, 2008. - A new method of normal approximation.
*Ann. Probab.,***36**no. 4, 1584-1610, 2008. - Estimation in spin glasses: A first step.
*Ann. Statist.,***35**no. 5, 1931-1946, 2007. - Concentration of Haar measures, with an application to random matrices.
*J. Funct. Anal.,***245**, 379-389, 2007. - Stein's method for concentration inequalities.
*Probab. Theory Related Fields,***138**, 305-321, 2007. - A generalization of the Lindeberg principle.
*Ann. Probab.,***34**no. 6, 2061-2076, 2006. -
Concentration inequalities with exchangeable pairs.
*Ph.D. thesis,*Stanford University, 2005. - Exchangeable pairs and Poisson approximation. (with Persi Diaconis and Elizabeth Meckes)
*Probab. Surv.,***2**, 64-106, 2005. - A new method for bounding rates of convergence of empirical spectral distributions. (with Arup Bose)
*J. Theoret. Probab.,***17**no. 4, 1003-1019, 2004. - Limiting spectral distributions of large dimensional random matrices. (with Arup Bose and Sreela Gangyopadhyay)
*J. Indian Statist. Assoc.,***41**no. 2, 221-259, 2003.

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