Books, Preprints, and Publications

Preprints

• On a generalisation of the coupon collector problem
  Joint work with Satyaki Mukherjee and Soumendu Sundar Mukherjee
  
  
• Path convergence of Markov chains on large graphs
  Joint work with Soumik Pal, Raghavendra Somani, Raghavendra Tripathi
  
  
• Controlled Martingale Problems And Their Markov Mimics
  Joint work with Vivek Borkar and Nitya Gadhiwala
  
  
• An Invariance Principle for a Random Walk Among Moving Traps via Thermodynamic Formalism
  Joint work with Alexander Drewitz and Rongfeng Sun.
  
  
  
• The Moran model with random resampling rates
  Joint work with Frank den Hollander, Adrian Röllin
  
  
• Sausage Volume of the Random String and Survival in a medium of Poisson Traps
  Joint work with Mathew Joseph and Carl Mueller
  
  
• Smoothness of Flow and Path-by-Path Uniqueness in Stochastic Differential Equations
  Joint work with Suprio Bhar and Atul Shekhar

Unpublished Manuscripts

• Blowup and Conditionings of $\psi$-super Brownian Exit Measures
  Joint work with Tom Salisbury
  
  
• Strategies to Mitigate COVID-19 Resurgence Assuming Immunity Waning: A Study for Karnataka, India
  Joint work with Aniruddha Adiga, Bryan Lewis, Madhav V. Marathe, Nihesh Rathod, Rajesh Sundaresan, Samarth Swarup, Srinivasan Venkatramanan and Sarath Yasodharan
  Slides
  
  
• Impact of Weeknight and Weekend Curfews Using Mobility Data: A Case Study Of Bengaluru Urban
  Joint work with Aniruddha Adiga, Madhav V. Marathe, Jagadish Midthala, Nihesh Rathod, Rajesh Sundaresan, Srinivasan Venkatramanan and Sarath Yasodharan
  

Books

• Draft-online:

  Probability and Statistics with Examples using R

  with Deepayan Sarkar, and Steve Tanner.
  
  

• Measure and Probability

  © Universities Press (India) 2008 ISBN 81 7371 613 7 Preface     Errata     Order Online

  © CRC Press (Outside India) 2009 ISBN 14 3980 126 6 Preface     Errata     Order Online

  with V.S. Sunder.
  
  

Publications

• Public Health

  1. A Multi-Team Multi-Model Collaborative Covid-19 Forecasting Hub for India
     Joint work with A Adiga, B Hurt, G Kaur, B Lewis, M Marathe, P Porebski et. al
     Appeared in 2023 Winter Simulation Conference (WSC), 994-1005
     
     
  2. Coupled models of genomic surveillance and evolving pandemics with applications for timely public health interventions
     Joint work with B Espinoza, A Adiga, S Venkatramanan, AS Warren, J Chen, BL Lewis et. al
     Appeared in Proceedings of the National Academy of Sciences 120 (48), November 2023.
     
     
  3. COVID-19 Modeling for India and a Roadmap for the Future
     Joint work with Rajesh Sundaresan and Gautam Menon
     Appeared in Communications of the ACM (November 2022)
     
     
     
     
  4. COVID-19: Optimal Design of Serosurveys for Disease Burden Estimation
     Joint work with Giridhara R. Babu, Aniruddha Iyer, Mohammed Minhaas B.S., Nihesh Rathod, Sharad Shriram, Rajesh Sundaresan, Nidhin Koshy Vaidhiyan, Sarath Yasodharan
     Slides, Survey Design Calculator
     Appeared in Sankhya B, The Indian Journal of Statistics. (August 24, 2021)
     
     
  5. Second round statewide survey for estimation of the burden of active infection and anti-SARS-CoV-2 IgG antibodies in the general population of Karnataka, India
     Joint work with Giridhara R. Babu,Rajesh Sundaresan et. al
     Appeared in IJID Regions. (October 30, 2021)
     
     
  6. [medrxiv] Effective Reproduction Number and Dispersion under Contact Tracing and Lockdown on COVID-19 in Karnataka
     Joint work with Nitya Gadhiwala and Abhiti Mishra
     Appeared in Journal of the Indian Society for Probability and Statistics (2021), Slides
     
     
  7. The burden of active infection and anti-SARS-CoV-2 IgG antibodies in the general population: Results from a statewide survey in Karnataka, India
     Joint work with Giridhara R Babu, Rajesh Sundaresan et. al
     Slides, Medrxiv Article,Supplementary Material,
     Appeared in International Journal of Infectious Diseases Vol. 108 p27-36 Published online: May 21, 2021

• Probability Theory

  1. Well-posedness of stochastic heat equation with distributional drift and skew stochastic heat equation
     Joint work with Oleg Butkovsky, Khoa Lê, Leonid Mytnik
     Appeared in Communications on Pure and Applied Mathematics 77 (5), 2708-2777 (2024).
     
     
  2. Volume Approximation of Strongly ${\mathbb C}$-Convex Domains by Random Polyhedra
     Joint work with Purvi Gupta and D. Yogeshwaran
     Appeared in Advances in Mathematics 432, 109243, (2023).
     
     
  3. Elliptic Harnack Inequality for ${\mathbb Z}^d$
     Joint work with Nitya Gadhiwala and Ritvik Radhakrishnan
     Appeared in Involve, a Journal of Mathematics 15 (4), 687-708 (2023).
     
     
  4. S.L.L.N. and C.L.T. for Random Walks in I.I.D. Random Environment on Cayley Trees
     Joint work with Antar Bandyopadhyay, Amites Dasgupta, Neeraja Sahasrabudhe
     Appeared in Stochastic Process and Their Applications Volume 146, April 2022, Pages 80-97.
     
     
  5. Small ball probabilities and a support theorem for the stochastic heat equation
     Joint work with Mathew Joseph and Carl Mueller
     Appeared in Ann. Probab. 49(5): 2548-2572 (September 2021). DOI: 10.1214/21-AOP1515
     
     
  6. Graphon-valued stochastic processes from population genetics
     Joint work with Frank den Hollander, Adrian Röllin
     Appeared in Ann. Appl. Probab. 31(4): 1724-1745 (August 2021). DOI: 10.1214/20-AAP1631
     
     
  7. Strong existence and uniqueness for stable stochastic differential equations with distributional drift
     Joint work with Oleg Butkovsky and Leonid Mytnik
     Appeared in Ann. Probab. 48 (2020), no. 1, 178-210.
     
     
  8. Central limit theorem for statistics of subcritical configuration models
     Joint work with D. Yogeshwaran
     Appeared in J. Ramanujan Math. Soc. 35 (2020), no. 2, 109-119.
     
     
  9. Random Walk Among Mobile/Immobile Traps: A Short Review.
     Joint work with Alexander Drewitz, and Rongfeng Sun.
     Appeared in Sojourns in Probability Theory and Statistical Physics - III: Interacting Particle Systems and Random Walks, A Festschrift for Charles M. Newman, 1-22. Springer Proceedings in Mathematics & Statistics, 300, 2019.
     
     
  10. Simultaneous Small Noise Limit for Singularly Perturbed Slow-Fast Coupled Diffusions
      Joint work with Vivek S. Borkar, K. Suresh Kumar, Rajesh Sundaresan
      Appeared in Applied Mathematics & Optimization (2019): 1-48.
      
      
  11. [ Arxiv]Respondent-driven sampling and sparse graph convergence
      Joint work with Adrian Röllin.
      Appeared in Electron. Commun. Probab. Volume 23 (2018), paper no. 3, 12 pp
      
      
  12. [ Arxiv] Harnack inequality for non-local Schrodinger operators
      Joint work with Koushik Ramachandran.
      Appeared in Potential Analysis May 2018, Volume 48, Issue 4, pp 515–551
      
      
  13. Invariance principle for variable speed random walks on trees
      Joint work with Wolfgang Löhr, Anita Winter.
      Appeared Ann. Probab. Volume 45, Number 2 (2017), 625-667.
      
      
  14. [ Arxiv] Subdiffusivity of a random walk among a Poisson system of moving traps on $\mathbb Z$
      Joint work with Alexander Drewitz and Rongfeng Sun.
      Appeared in Mathematical Physics, Analysis and Geometry 20, Article 1, 2017.
      
      
  15. [ Arxiv ] The gap between Gromov-vague and Gromov-Hausdorff-vague topology
      Joint work with Wolfgang Löhr, Anita Winter.
      Appeared in Stochastic Processes and their Applications 126 (2016) 2527-2553
      
      
  16. [ Arxiv] Dense graph limits under respondent-driven sampling
      Joint work with Adrian Röllin.
      Appeared in Annals of Applied Probability 2016, Vol 26, No. 4, 2193-2210.
      
      
  17. Random Walks in I.I.D. Random Environment on Non-Abelian Free Groups
      Joint work with Antar Bandhyopadyay and Amites Dasgupta.
      Appeared in Statist. Probab. Lett., 92: 39 - 44, 2014
      
      
  18. Brownian motion on ${\mathbb R}$ trees
      Joint work with Michael Eckhoff and Anita Winter
      Appeared in Transaction American Mathematics Society Vol 365, 2013, 3115-3150.
      
      
  19. Systems of branching, annihilating, and coalescing particles
      Joint work with Jan Swart
      Appeared in Electron. J. Probab. Volume 17 (2012), paper no. 80, 32 pp.
      
      
  20. One dimensional voter model interface revisited
      Joint work with Rongfeng Sun
      Appeared in Electronic Communications in Probability, Vol. 16(2011), Paper 70
      
      
  21. On the Range, local times and periodicity of random walk on an interval
      Joint work with Sunder Sethuraman and Balint Toth
      Appeared in ALEA, Latin American Journal of Probability and Mathematical Statistics, Volume VIII, 2011, Pages, 269-284.
      
      
  22. Super-critical Age Dependent Branching Markov Processes and Their Scaling Limits
      Joint work with Krishna Athreya and Srikanth Iyer.
      Appeared in Bernoulli Volume 17, Number 1 (2011), 138-154.
      
      
  23. Critical Age Dependent Branching Markov Processes and Their Scaling Limits
      Joint work with Krishna Athreya and Srikanth Iyer.
      Appeared in the Proceedings of the Indian Academy of Sciences, Volume 120, Number 3, June 2010 , pp. 363-385(23).
      
      
  24. Survival of Contact Processes on the Hierarchical Group
      Joint work with Jan Swart
      Appeared in Probability Theory and Related Fields (online first)
      
      
  25. Exit time, Green Function and Semilinear Elliptic Equations.
      Joint work with Rami Atar and Zhen-Qing Chen
      Appeared in Electronic Journal in Probability, Vol 14, p 51-70, Jan 2009
      
      
  26. Random Directed Trees and Forest
      Joint work with Rahul Roy and Anish Sarkar
      Appeared in Electronic Journal in Probability, Vol 13, p 2160-2189, Dec 2008
      
      
  27. Quantifying spatial misallocation in centrally provided public goods
      Joint work with Rohini Somanathan.
      Appeared in Economic Letters 98 (2), p.201-206, Feb 2008.
      
      
  28. Erratum: "Infinite volume limit for the stationary distribution of abelian sandpile models"
      Joint work with Antal Jarai
      Appeared in Comm. Math. Phys. 264 (2006), no. 3, 843.
      
      
  29. Infinite dimensional stochastic differential equations of the Ornstein-Uhlenbeck type.
      Joint work with Richard Bass, Masha Gordina and Edwin Perkins
      Appeared in Stochastic Process. Appl. 116 (2006), no. 3, 381--406.
      
      
      
  30. Spatial Coupling of Measure valued neutral models
      Joint work with Anita Winter.
      Appeared in Stochastic Process. Appl. 115 (2005), no. 6, 891--906
      
      
  31. Branching-coalescing Particle Systems
      Joint work with Jan Swart.
      Appeared in Probab. Theory Related Fields 131 (2005), no. 3, 376--414.
      
      Correction :There is an error in the above paper in Theorem 7. A correct version of Theorem 7 has been put on the ArXiv
      
      
  32. Hölder norm estimates for elliptic operators on finite and infinite dimensional spaces
      Joint work with Richard Bass and Edwin Perkins
      Appeared in Trans. Amer. Math. Soc. 357 (2005), no. 12, 5001--5029.
      
      
  33. Infinite volume limit for the stationary distribution of Abelian sandpile models
      Joint work with Antal Jarai.
      Appeared in Communications in Mathematical Physics
      
      
  34. On the coverage of space by random sets.
      Joint work with Rahul Roy and Anish Sarkar.
      Appeared in Advances in Applied Probability (36),1, 2004.
      
      
  35. Degenerate Stochastic differential equations and super-Markov chains
      Joint work with Martin Barlow, Richard Bass, and Edwin Perkins.
      Appeared in Probability Theory and Related Fields, (123), 484-520, 2002.
      
      
  36. On a Singular Semilinear Elliptic Boundary Value Problem and the Boundary Harnack Principle
      Appeared in Potential Analysis (17), 293-301, 2002
      [This paper was part of my thesis work under Chris Burdzy.]
      
      
  37. Uniqueness for a class of one-dimensional Stochastic PDEs using Moment Duality
      Joint work with Roger Tribe
      Appeared in Annals of Probability,(28),4,1711-1734, 2002
      
      
  38. Ballistic Deposition in a planar strip
      Joint work with Rami Atar and Min Kang.
      Appeared in Electronic communications of Probability , Vol. 6, Paper no. 3, pages 31-38, 2001.
      
      
  39. Monotonicity Property for a Class of Semilinear Partial Differential Equations.
      Appeared in Seminar de's probabilite's XXXIV (june 2000)
      [ This paper was part of my thesis work under Chris Burdzy.]