- 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, Berlin-Heidelberg, 2014.
Preprints and submitted papers
- Proof of the path localization conjecture for directed polymers.
- Yang-Mills for probabilists.
- Central limit theorem for the free energy of the random field Ising model.
- Rigidity of the three-dimensional hierarchical Coulomb gas.
- The endpoint distribution of directed polymers. (with Erik Bates)
- 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)
- Localization in random geometric graphs with too many edges. (with Matan Harel)
- Stochastic solutions of the wave equation.
- Assumptionless consistency of the Lasso.
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.
Published or accepted papers
- A general method for lower bounds on fluctuations of random variables. To appear in Ann. Probab.
- Rigorous solution of strongly coupled SO(N) lattice gauge theory in the large N limit. To appear in Comm. Math. Phys.
- On the decay of correlations in the random field Ising model. To appear in Comm. Math. Phys.
- Arbitrarily small perturbations of Dirichlet Laplacians are quantum unique ergodic. (with Jeffrey Galkowski) To appear in J. Spectr. Theory.
- On level sets of Gaussian fields. (with Amir Dembo and Jian Ding) To appear in Electr. Commun. Probab.
- Properties of Uniform Doubly Stochastic Matrices (with Persi Diaconis and Allan Sly) To appear in Ann. de l'Inst. Henri Poincaré.
- 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.