Research Interests

My main interests as of now are in problems at the intersection of discrete probability, networks and statistical physics. My main aim is to learn and use the powerful tools of probability to tell me useful things about the real world.

More precisely my interests include

  • random networks, dynamics on random networks, spatially optimal networks, probabilistic combinatorial optimization, reconstruction of real world networks, percolation, critical phenomenon and phase transitions.
  • understanding the relation between phase transitions in statistical physics and its effect on the performance of randomized algorithms.
  • interface between the above fields of study and the applied branches of science including computer science, biology, statistics and physics.

 

Preprints

Arranged in reverse chronological order

  1. Title: Weakly interacting particle systems on inhomogeneous random graphs
    co-authors: Amarjit Budhiraja, Ruoyu Wu
    Published: Arxiv version
    Remarks: Arxiv version: December 2016.
  2. Title: Large subgraphs in pseudo-random graphs
    co-authors: Anirban Basak, Suman Chakraborty, Andrew Nobel
    Published: Arxiv version
    Remarks: Arxiv version: December 2016.
  3. Title: Geometry of the Vacant set Left by Random Walk on Random Graphs, Wright’s Constants, and Critical Random Graphs With Prescribed Degrees
    co-authors: Sanchayan Sen
    Published: Arxiv version
    Remarks: Arxiv version: August 2016.
  4. Title: The Continuous Configuration Model: A Null for Community Detection on Weighted Networks
    co-authors: John Palowitch, Andrew B. Nobel.
    Published: Arxiv version
    Remarks: Arxiv version: January 2016.
    Comments: Code and supplemental info available at this http URL
  5. Title: Scaling limits of random graph models at criticality: Universality and the basin of attraction of the Erdos-Renyi random graph.
     co-authors: Nicolas Broutin, Sanchayan Sen and Xuan Wang.
     Published: Arxiv preprint
    Remarks: Arxiv version: November 2014.
  6. Title: Universal techniques to analyze preferential attachment tree and networks: Global and Local analysis
    Published: To be submitted to Probability Surveys  .pdf version
    Verbal Description:.pdf version.
    Remarks: This is a long paper trying to develop a unified set of tools for tackling many different models. I shall be preparing a shorter version more amenable for publication soon.

 

Accepted Papers

Arranged in reverse chronological order.

 

  1. Title: Change point detection in Network models: Preferential attachment and long range dependence
    co-authors: Jimmy Jin, Andrew Nobel.
    Published: Accepted in Annals of Applied Probability (2017).
    Remarks: Arxiv version: 2015.
  2. Title: Diameter of the Stochastic mean field model of distance
    co-authors: Remco van der Hofstad
    Published: Accepted in Combinatorics, Probability and Computing (2017).  Arxiv version
    Remarks:
  3. Title: Critical Random Graphs and the Differential Equations Technique.
    co-authors: Amarjit Budhiraja and Sanchayan Sen
    Published: Accepted in Indian Journal of Pure and Applied Mathematics (2017)
    Remarks:
  4. Title: Energy Landscape for large average submatrix detection problems in gaussian random matrices.
    co-authors: Partha Dey and Andrew Nobel
    Published: Accepted in Probability Theory and Related Fields (2017).pdf version
    Remarks: Arxiv version: November 2012.
  5. Title: The multiplicative coalescent, inhomogeneous continuum random trees, and new universality classes for critical random graphs
    co-authors: Sanchayan Sen and Remo van der Hofstad.
    Published:  Accepted in Probability Theory and Related Fields (2017) Arxiv version
    Remarks: Arxiv version: 2015.
  6. Title: Stochastic Weighted Graphs: Flexible Model Specification and Simulation
    co-authors: James D. Wilson, Matthew J. Denny, Shankar Bhamidi, Skyler Cranmer, Bruce Desmarais
    Published: Accepted in Social Networks, 2016
    Remarks: Arxiv version: 2015.
  7. Title: Continuum limit of inhomogenous random graphs
    co-authors: Sanchayan Sen and Xuan Wang.
    Published: Accepted in Probability Theory and Related Fields, 2016
    Remarks: Arxiv version: April 2014.
  8. Title: Universality for first passage percolation on sparse random graphs
    co-authors: Remco van der Hofstad and Gerard Hooghiemstra
    Published: Accepted in Annals of Probability, 2016 .pdf version
  9. Title: Childhood peer network characteristics: genetic influences and links with early mental health trajectories
    co-authors: Eszter Szekely,Irene Pappa, James D. Wilson, Vincent W. Jaddoe, Frank C. Verhulst, Henning Tiemeier, Philip Shaw
    Published: Appeared in Journal of Child Psychology and Psychiatry, 2015
  10. Title: Exceptional rotations of random graphs: a VC theory
    co-authors:Louigi Addario-Berry, Sebastien Bubeck, Luc Devroye, Gabor Lugosi, Roberto Imbuzeiro Oliveira
    Published: Appeared in Journal of Machine Learning Research, 2015
  11. Title: The importance sampling technique for understanding rare events in Erdos-Renyi random graphs
    co-authors: Jan Hannig, Chia Ying Lee, James Nolen
    Published: Accepted in Electronic Journal of Probability, 2015 .pdf version
    Verbal Description:Remarks: Arxiv version: February 2013.
  12. Title: Twitter event networks and the superstar model
    co-authors: J.Michael Steele and Tauhid Zaman
    Published: Accepted in Annals of Applied Probability .pdf version
    Verbal Description:Remarks: 2014
  13. Title: A Testing Based Extraction Algorithm for Identifying Significant Communities in Networks
    co-authors: James D. Wilson, Simi Wang, Peter J. Mucha, Andrew B. Nobel
    Published: Accepted in Annals of Applied Statistics Arxiv version
    Verbal Description:Remarks: 2014
  14. Title: Degree distribution of shortest path trees and bias of network sampling algorithms
    co-authors: Jesse Goodman and Remco van der Hofstad and Julia Komjathy
    Published: Accepted in Annals of Applied Probability, 2014, .pdf versionVerbal Description:
    Remarks: April 2014
  15. Title: The front of the epidemic curve and first passage percolation
    co-authors: Remco van der Hofstad and Julia Komjáthy
    Published: Accepted in the Journal of Applied Probability, .pdf version
    Verbal Description:Remarks: April 2014.
  16. Title: Bounded-size rules: The barely subcritical regime
    co-authors: Amarjit Budhiraja and Xuan Wang
    Published: Accepted in Combinatorics Probability and Computing .pdf version
    Verbal Description:Remarks: March 2014.
  17. Title: The augmented multiplicative coalescent, bounded size rules and critical dynamics of random graphs
    co-authors: Amarjit Budhiraja and Xuan Wang
    Published: Accepted in Probability Theory and Related Fields. .pdf version
    Verbal Description:Remarks: November 2013.
  18. Title: Measuring the Statistical Significance of Local Connections in Directed Networks
    co-authors: James Wilson and Andrew Nobel
    Published: Accepted in NIPS Workshop on Frontiers of Network Analysis: Methods, Models, and Applications .pdf versionVerbal Description:
    Remarks: December 2013.
  19. Title: Functional Data Analysis of Tree Data Objects
    co-authors: Dan Shen, Haipeng Shen, Yolanda Munoz Maldonado, Yongdai Kim, and J. S. Marron
    Published: Journal of Computational and Graphical Statistics. .pdf version
    Verbal Description:
    Remarks: 2013
  20. Title: Aggregation models with limited choice and the multiplicative coalescent
    co-authors: Amarjit Budhiraja and Xuan Wang
    Published: Accepted in Random Structures and Algorithms .pdf version
    Verbal Description:Remarks: This article considers the Bohman-Frieze process which is a dynamic way of constructing a network via the inclusion of edges, wherein one incorporates the effect of choice in the selection the edge. The exact nature of the emergence of the giant component has been open since the formulation of the model in 2001. Using a technique very different from the usual breadth-first search technique we analyze exactly what happens at criticality.
  21. Title: Weak disorder in the stochastic mean-field model of distance II
    co-authors: Remco van der Hofstad and Gerard Hooghiemstra
    Published: Accepted in Bernoulli .pdf version
    Remarks: This paper deals with the case where each edge in the complete graph has E^s edge weight, where s is negative. It turns out that the behavior of the optimal paths between vertices is completely different from the s positive case. This was also the first time that we have used Stein’s method for Poisson approximation to get delicate quantitative results for extrema in first passage percolation.
  22. Title: First Passage Percolation on Erdos-Renyi random graphs
    co-authors: Remco van der Hofstad and Gerard Hooghiemstra
    Published: Accepted in Combinatorics, Probability and Computing .pdf version
    Remarks: This extends our treatment of first passage percolation on the configuration model to the case of the Erdos-Renyi random graphs and completes the treatment of this model in all regimes of the edge connection probability p.
  23. Title: Variants of Brownian Motion
    co-authors: Priscilla Greenwood
    Published: Accepted in the Wiley OR Encyclopedia
    Remarks: This is an introductory encyclopedia article on various variants of Brownian Motion.
  24. Title: Weak disorder in the stochastic mean field model of distance
    co-authors: Remco van der Hofstad
    Published: Accepted in the Annals of Applied Probability .pdf version
    Verbal Description:.pdf version
  25. Title: Novel scaling limits for critical inhomogeneous random graphs
    co-authors: Remco van der Hofstad and Johan van Leeuwaarden
    Published: Accepted in Annals of Probability .pdf version
    Verbal Description:.pdf version
  26. Title: Scaling limits for critical inhomogeneous random graphs with finite third moments
    co-authors: Remco van der Hofstad and Johan van Leeuwaarden
    Published: Accepted in Electronic Journal of Probability .pdf version
    Verbal Description:.pdf version
  27. Title: Extreme value theory, Poisson Dirichlet distributions and first passage percolation on random networks
    co-authors: Remco van der Hofstad and Gerard Hooghiemstra
    Published: Accepted in Advances in Applied probability .pdf version
    Verbal Description:.pdf version.
    Remarks: This completes the study of first passage percolation on the configuration model.
  28. Title: First passage percolation on random graphs with finite mean degrees
    co-authors: Remco van der Hofstad and Gerard Hooghiemstra
    Published: Accepted in Annals of Applied probability .pdf version
    Verbal Description:.pdf version.
    Remarks: This is part of a general scheme to understand how disorder changes the inherent graph geometry of random graph models.
  29. Title: Mixing time of exponential random graphs
    co-authors: Guy Bresler and Allan Sly
    Published: Accepted in Annals of Applied probability .pdf version
    Verbal Description:.pdf version.
    Remarks: Full version
  30. Title: Mixing time of exponential random graphs
    co-authors: Guy Bresler and Allan Sly
    Published: Accepted in FOCS 2008 .pdf version
    Verbal Description:.pdf version.
    Remarks: Extended Abstract
  31. Title: Spectra of Random Trees
    co-authors: Steve Evans and Arnab Sen
    Published: Accepted in Journal of Theoretical Probability .pdf version
    Verbal Description:.pdf version.
  32. Title: First passage percolation on locally tree like networks I: Dense random graphs
    Published: Accepted in the Special Issue on Statistical Mechanics of Random Structures, Journal of Mathematical Physics (2008) .pdf version
    Verbal Description:.pdf version.
  33. Title: Network Delay Inference from Additive Metrics
    co-authors: Ram Rajagopal and Sebastien Roch
    Published: Accepted in Random Structures and Algorithms .pdf version
    Verbal Description:.pdf version.
  34. Title: Edge Flows on the complete random edge lengths network
    co-author: David Aldous
    Published: Accepted in Random Structures and Algorithms .pdf version.
    Verbal Description:.pdf version.
  35. Title: Brownian motion on disconnected sets, basic hypergeometric functions, and some continued fractions of Ramanujan
    co-authors: Steve Evans, Ron Peled, and Peter Ralph.
    Published IMS Collections Probability and Statistics: Essays in Honor of David A. Freedman Vol. 2 (2008) 42–75 .pdf version
    Verbal Description: .pdf version.