# Research

My research interests are in nonparametric statistics, combinatorial probability, and discrete and computational geometry. Here is a link to my CV. See also arXiv, DBLP, and MathSciNet.

## Statistics and Applications

### Distribution-Free and Nearest-Neighbor Methods for Nonparametric Inference

• Efficiency lower bounds for distribution-free Hotelling-type two-sample tests based on optimal transport (with Nabarun Deb and Bodhisattva Sen), 2022. (arXiv)
• Distribution-free multisample test based on optimal matching with applications to single cell genomics (with Divyansh Agarwal, Somabha Mukherjee, and Nancy R. Zhang), Journal of the American Statistical Association, Vol. 117 (538), 627-638, 2022. (arXiv, Journal)
• A nearest-neighbor based nonparametric test for viral remodeling in heterogeneous single-cell proteomic data (with Trambak Banerjee and Gourab Mukherjee), Annals of Applied Statistics, Vol.14 (4), 1777-1805, 2020. (arXiv, Journal)
• Asymptotic distribution and detection thresholds for two-sample tests based on geometric graphs, Annals of Statistics, Vol. 48 (5), 2879–2903, 2020. (arXiv, Journal)
• A general asymptotic framework for distribution-free graph-based two-sample tests, Journal of the Royal Statistical Society, Series B, 575-602, Vol. 81 (3), 2019. (arXiv, Journal)

### Inference in Graphical Models

• High dimensional logistic regression under network dependence (with Somabha Mukherjee, Sagnik Halder, and George Michailidis), 2021. (arXiv)
• Phase transitions of the maximum likelihood estimates in the p-spin Curie-Weiss model (with Somabha Mukherjee and Jaesung Son), 2020. (arXiv)
• Estimation in tensor Ising models (with Somabha Mukherjee and Jaesung Son), Information and Inference: A Journal of the IMA, to appear, 2022. (arXiv, Journal)
• Parameter estimation for undirected graphical models with hard constraints (with Kavita Ramanan), IEEE Transactions on Information Theory, Vol. 67 (10), 6790-6809, 2021. (arXiv, Journal)
• Inference in Ising models (with Sumit Mukherjee), Bernoulli, Vol. 24 (1), 493-525, 2018. (arXiv, Journal)

### Graphons and Network Analysis

• Fluctuations of subgraph counts in graphon based random graphs (with Anirban Chatterjee and Svante Janson), 2022. (arXiv)
• Motif estimation via subgraph sampling: the fourth moment phenomenon (with Sayan Das and Sumit Mukherjee), Annals of Statistics, Vol. 50 (2), 987-1011, 2022. (arXiv, Journal)
• Goodness-of-fit tests for inhomogeneous random graphs (with Soham Dan), International Conference on Machine Learning (ICML), PMLR 119, 2335-2344, 2020. (Proceedings)

### Observational Studies

• A nonparametric likelihood approach for inference in instrumental variable models (with Kwonsang Lee, Jing Qin, and Dylan Small), 2019. (arXiv)
• Sensitivity analysis for inverse probability weighting estimators via the percentile bootstrap (with Qingyuan Zhao and Dylan Small), Journal of the Royal Statistical Society, Series B, Vol. 81 (4), 735–761, 2019. (arXiv, Journal)

### Miscellaneous

• Predicting X-sensitivity of circuit-inputs on test-coverage: A machine-learning approach, (with Manjari Pradhan, Krishnendu Chakraborty, and Bhargab B. Bhattacharya), IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems (TCAD), Vol. 38 (12), 2343–2356, 2019. (Journal)
• The projection median of a set of points in $\mathbb R^d$ (with Riddhipratim Basu and Tanmoy Talukdar), Discrete and Computational Geometry, Vol. 47 (2), 329–346, 2012. (PDF, Journal)

## Combinatorics and Probability

### Random Multilinear Forms, Graph Coloring, and Second/Fourth-Moment Theorems

• Asymptotic distribution of random quadratic forms (with Sayan Das, Somabha Mukherjee, and Sumit Mukherjee), 2022. (arXiv)
• Normal approximation and fourth moment theorems for monochromatic triangles (with Xiao Fang and Han Yan), Random Structures and Algorithms, Vol. 60 (1), 25-53, 2022. (arXiv, Journal)
• Asymptotic distribution of Bernoulli quadratic forms (with Somabha Mukherjee and Sumit Mukherjee), Annals of Applied Probability, Vol. 31 (4), 1548-1597, 2021. (arXiv, Journal)
• The second moment phenomenon for monochromatic subgraphs (with Somabha Mukherjee and Sumit Mukherjee), SIAM Journal on Discrete Mathematics, Vol. 34 (1), 794-824, 2020. (arXiv, Journal)
• Limit theorems for monochromatic stars (with Sumit Mukherjee), Random Structures and Algorithms, Vol. 55 (4), 831–853, 2019. (arXiv, Journal)
• Monochromatic subgraphs in randomly colored graphons (with Sumit Mukherjee), European Journal of Combinatorics, Vol. 81, 328-353, 2019. (arXiv, Journal)
• Universal Poisson and Normal limit theorems in graph coloring problems with connections to extremal combinatorics (with Persi Diaconis and Sumit Mukherjee), Annals of Applied Probability, Vol. 27 (1), 337-394, 2017. (arXiv, Journal)
• Collision times in multicolor urn models and sequential graph coloring with applications to discrete logarithms, Annals of Applied Probability, Vol. 26 (6), 3286-3318, 2016. (arXiv, Journal)

### Mean-Field Statistical Physics Models

• Fluctuations of the magnetization in the p-spin Curie-Weiss model (with Somabha Mukherjee and Jaesung Son), Communications in Mathematical Physics, Vol. 387, 681-728, 2021. (PDF, Journal)
• High temperature asymptotics of orthogonal mean-field spin glasses (with Subhabrata Sen), Journal of Statistical Physics, Vol. 162 (1), 63-80, 2016. (arXiv, Journal)

### Miscellaneous

• Degree sequence of random permutation graphs (with Sumit Mukherjee), Annals of Applied Probability, Vol. 27 (1), 439-484, 2017. (arXiv, Journal)
• Exact and asymptotic results on coarse Ricci curvature of graphs (with Sumit Mukherjee), Discrete Mathematics, Vol. 338, 23–42, 2015. (arXiv, Journal)
• Minimum-weight edge discriminator in hypergraphs (with Sayantan Das and Shirshendu Ganguly), Electronic Journal of Combinatorics, Vol. 21 (3), #P3.18, 2014. (arXiv, Journal)

## Discrete and Computational Geometry

### Facility Location and Voronoi Games

• The $1$-Dimensional discrete Voronoi game (with Aritra Banik, Sandip Das, and Sreeja Das), Operations Research Letters, Vol. 47, 115-121, 2019. (PDF, Journal)
• The discrete Voronoi game in $\mathbb R^2$ (with Aritra Banik, Sandip Das, and Satyaki Mukherjee), Computational Geometry: Theory and Applications, Vol. 63, 53-62, 2017. (PDF, Journal)
• The minimum enclosing circle of a set of fixed points and a mobile point (with Aritra Banik and Sandip Das), Computational Geometry: Theory and Applications, Vol. 47 (9), 891–898, 2014. (PDF, Journal)
• Optimal strategies for the one-round discrete Voronoi game on a line (with Aritra Banik and Sandip Das), Journal of Combinatorial Optimization, Vol. 26, 655-669, 2013. (PDF, Journal)
• New variations of the maximum coverage facility location problem (with Subhas C. Nandy), European Journal of Operational Research, Vol. 224, 477-485, 2013. (PDF, Journal)
• On the Fermat-Weber point of a polygonal chain and its generalizations, Fundamenta Informaticae, Vol. 107 (4), 331-343, 2011. (arXiv, Journal, Mathematica Demo)
• Maximizing Voronoi regions of a set of points enclosed in a circle with applications to facility location, Journal of Mathematical Modelling and Algorithms, Vol. 9 (4), 375-392, 2010. (PDF, Journal)

### Erdős-Szekeres and Geometric Ramsey Problems

• Almost empty monochromatic triangles in planar point sets (with Deepan Basu, Kinjal Basu, and Sandip Das), Discrete Applied Mathematics, Vol. 210, 207-213, 2016. (arXiv, Journal)
• On pseudo-convex partitions of a planar point set (with Sandip Das), Discrete Mathematics, Vol. 313 (21), 2401–2408, 2013. (arXiv, Journal)
• Disjoint empty convex pentagons in planar point sets (with Sandip Das), Periodica Mathematica Hungarica, Vol. 66 (1), 73–86, 2013. (arXiv, Journal)
• Holes or empty pseudo-triangles in planar point sets (with Sandip Das), Moscow Journal of Combinatorics and Number Theory, Vol. 2 (1), 16-46, 2012. (arXiv, Journal)
• On the minimum size of a point set containing a 4-Hole and a disjoint 5-Hole (with Sandip Das), Studia Scientiarum Mathematicarum Hungarica, Vol. 48 (4), 445-457, 2012. (PDF, Journal)
• Geometric proof of a Ramsey-type result for disjoint empty convex polygons I and II (with Sandip Das), Geombinatorics, Vol. XX (1), 5–16, and Vol. XIX (4), 2010. (PDF I, PDF II)