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Research

I work on interacting particle systems, ergodic properties of diffusions and stochastic networks,  reconstruction algorithms on dynamic random networks and probabilistic couplings.

My research is supported by the NSF CAREER award DMS 2141621. I am also a co-PI on the NSF RTG grant DMS 2134107.

Submitted articles

  1. Flocking under Fast and Large Jumps: Stability, Chaos, and Traveling Waves (with A. Budhiraja and D. Imon) arXiv preprint arXiv: 2404.13117, 52 pages, 2024.
  2. Local weak convergence and its applications (with S. Bhamidi, J. Shen and S. P. Young) arXiv preprint arXiv: 2403.01544, 33 pages, 2024.
  3. Fluctuations of the Atlas model from inhomogeneous stationary profiles (with A. Budhiraja and P. Rudzis) arXiv preprint arXiv: 2310.04545, 58 pages, 2023.
  4. Attribute network models, stochastic approximation, and network sampling and ranking algorithms (with N. Antunes, S. Bhamidi and V. Pipiras) arXiv preprint arXiv: 2304.08565, 48 pages, 2023.
  5. Local weak limits for collapsed branching processes with random out-degrees (with P. Deka and M. Olvera-Cravioto) arXiv preprint arXiv: 2302.00562,  23 pages, 2023.
  6. Long time behavior of finite and infinite dimensional reflected Brownian motions (with A. Budhiraja) arXiv preprint arXiv: 2208.02855,  27 pages, 2022.
  7. Extremal invariant distributions for infinite Brownian particle systems with rank dependent drifts (with A. Budhiraja) arXiv preprint arXiv: 2207.08331, 24 pages, 2022.
  8. Many-server asymptotics for Join-the-Shortest Queue in the Super-Halfin-Whitt Scaling Window (with Z. Zhao and D. Mukherjee) arXiv preprint arXiv: 2106.00121, 69 pages, 2021.

Published and accepted articles

  1. Co-evolving dynamic networks (with S. Bhamidi and X. Huang) Probability Theory and Related Fields (to appear), arXiv preprint arXiv: 2203.11877, 60 pages, 2024.
  2. Load Balancing in Parallel Queues and Rank-based Diffusions (with A. Budhiraja and B. Estevez) Mathematics of Operations Research (to appear), arXiv preprint arXiv: 2302.10317, 36 pages, 2024.
  3. Learning Attribute and Homophily Measures Through Random Walks (with N. Antunes, S. Bhamidi and V. Pipiras), Applied Network Science (2023), 26 pages.
  4. PageRank Nibble on the sparse directed stochastic block model (with P. Deka  and M. Olvera-Cravioto) Proceedings of the 18th Workshop on Algorithms and Models for the Web Graph, Toronto, Canada, March 2023. Available at arXiv:2303.06699, 17 pages, 2023.
  5. Degree centrality and root finding in growing random networks (with X. Huang) Electronic Journal of Probability, 2023, Vol. 28, paper no. 42, 1-39.
  6. The Inert Drift Atlas Model (with A. Budhiraja and B. Estevez) Communications in Mathematical Physics, https://doi.org/10.1007/s00220-022-04589-2. Available at arXiv: 2202.05893, 55 pages, 2022.
  7. Fluctuation bounds for continuous time branching processes and nonparametric change point detection in growing networks (with S. Bhamidi and I. Carmichael) The Annals of Applied Probability, to appear. Available at arXiv: 1808.02439, 57 pages, 2022.
  8. Dimension-free local convergence and perturbations for reflected Brownian motions (with B. Brown) The Annals of Applied Probability, 33(1): 376-416 (February 2023). DOI: 10.1214/22-AAP1818. Available at arXiv: 2009.12937.
  9. Domains of attraction of invariant distributions of the infinite Atlas model (with A. Budhiraja) The Annals of Probability, 50(4): 1610-1646 (July 2022). DOI: 10.1214/22-AOP1570. Available at arXiv: 2103.10508.
  10. PageRank asymptotics on directed preferential attachment networks (with M. Olvera-Cravioto) The Annals of Applied Probability, 32(4): 3060–3084 (2022). DOI: 10.1214/21-AAP1757. Available at arXiv: 2102.08894.
  11. Heavy Traffic Scaling Limits for shortest remaining processing time queues with heavy tailed processing time distributions (with A, Budhiraja and A. Puha) The Annals of Applied Probability, 32(4): 2587-2651 (August 2022). DOI: 10.1214/21-AAP1741. Available at arXiv: 2003.03655.
  12. Root finding algorithms and persistence of Jordan centrality in growing random trees (with S. Bhamidi) The Annals of Applied Probability, 32(3): 2180-2210 (June 2022). DOI: 10.1214/21-AAP1731. Available at arXiv: 2006.15609.
  13. Persistence of hubs in growing random networks (with S. Bhamidi) Probability Theory and Related Fields 180, 891–953 (2021). https://doi.org/10.1007/s00440-021-01066-0.
  14. Ergodicity and steady state analysis of Interference queueing networks (with A. Sankararaman) AMS Contemporary Mathematics: Special volume in honor of M. M. Rao, to appear, arXiv preprint arXiv: 2005.13051, 12 pages, 2021.
  15. Rates of convergence to equilibrium for Potlatch and Smoothing processes (with K. Burdzy) The Annals of Probability 49(3): 1129-1163 (May 2021). DOI: 10.1214/20-AOP1473.
  16. Large Deviations from the hydrodynamic limit for a system with Nearest Neighbor Interactions (with A. Budhiraja and M. Perlmutter) Electron. J. Probab. 25 (2020), no. 26, https://doi.org/10.1214/20-EJP434, 51 pages, 2020.
  17. Inert drift system in a viscous fluid: Steady state asymptotics and exponential ergodicity (with B. Brown) Trans. Amer. Math. Soc. 373 (2020), 6369-6409, DOI: https://doi.org/10.1090/tran/8098.
  18. Parameter and dimension dependence of convergence rates to stationarity for Reflecting Brownian Motions (with A. Budhiraja) The Annals of Applied Probability 30(5): 2005-2029 (October 2020). DOI: 10.1214/19-AAP1550.
  19. Join-the-Shortest Queue Diffusion Limit in Halfin-Whitt Regime: Sensitivity on the Heavy-traffic Parameter (with D. Mukherjee) The Annals of Applied Probability30(1): 80-144 (February 2020). DOI: 10.1214/19-AAP1496.
  20. Join-the-Shortest Queue Diffusion Limit in Halfin-Whitt Regime: Tail Asymptotics and Scaling of Extrema (with D. Mukherjee). The Annals of Applied Probability29(2): 1262-1309 (April 2019). DOI: 10.1214/18-AAP1436.
  21. Coupling Polynomial Stratonovich Integrals: the two-dimensional Brownian case (with W.S. Kendall). Electronic Journal of Probability, 2018, Vol. 23, paper no. 24, 1-43.
  22. Gravitation versus Brownian motion (with K. Burdzy and M. Duarte). Annales de l’Institut Henri Poincaré 55 (2019), no. 3, 1531–1565. doi:10.1214/18-AIHP927.
  23. Coupling in the Heisenberg group and its application to gradient estimates (with M. Gordina and P. Mariano). The Annals of Probability, 2018, Vol. 46, No. 6, 3275-3312.
  24. Coupling the Kolmogorov Diffusion: maximality and efficiency considerations (with W.S. Kendall). Advances in Applied Probability 48A, 21 pages, 2016 (to appear).
  25. Rigidity for Markovian Maximal Couplings of Elliptic Diffusions (with W.S. Kendall). Probability Theory and Related Fields, pages 1-58, 2016. DOI:10.1007/s00440-016-0706-4
  26. Random mass splitting and a quenched invariance principle (with C. Hoffman). Stochastic Processes and their Applications, 126(2): pages 608-627, 2016.
  27. The Brownian Conga Line. Probability Theory and Related Fields. August 2016, Volume 165, Issue 3, pp 901–961.
  28. Noncrossing partitions, Catalan words, and the Semicircle Law (with A. Bose). Journal of Theoretical Probability. June 2013, Volume 26, Issue 2, pp 386-409.

Ph.D. Thesis

On Particle Interaction Models

Unpublished notes

1.  Brownian motion with boundary diffusion

2.  Heteroscedastic Wigner matrices (with A. Bose and S. Sen).