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: Continuum limit of inhomogenous random graphs

    co-authors: Sanchayan Sen and Xuan Wang.

    Published: Submitted Arxiv version

    Verbal Description:

    Remarks: Arxiv version: April 2014.

  2. Title: Diameter of the Stochastic mean field model of distance

    co-authors: Remco van der Hofstad

    Published: Submitted Arxiv version

    Verbal Description:

    Remarks: Arxiv version: June 2013.

  3. Title: The importance sampling technique for understanding rare events in Erdos-Renyi random graphs

    co-authors: Jan Hannig, Chia Ying Lee, James Nolen

    Published: Submitted .pdf version

    Verbal Description:

    Remarks: Arxiv version: February 2013.

  4. Title: Energy Landscape for large average submatrix detection problems in gaussian random matrices.

    co-authors: Partha Dey and Andrew Nobel

    Published: Submitted .pdf version

    Verbal Description:

    Remarks: Arxiv version: November 2012.

  5. Title: Universality for first passage percolation on sparse random graphs

    co-authors: Remco van der Hofstad and Gerard Hooghiemstra

    Published: Submitted .pdf version

    Verbal Description:

    Remarks: Arxiv version: October 2012.

  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: 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

  2. 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

  3. 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 version

    Verbal Description:

    Remarks: April 2014

  4. 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.

  5. 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.

  6. 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.

  7. 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 version

    Verbal Description:

    Remarks: December 2013.

  8. 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

  9. 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.

  10. 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

    Verbal Description:

    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.

  11. 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

    Verbal Description:

    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.

  12. Title: Variants of Brownian Motion

    co-authors: Priscilla Greenwood

    Published: Accepted in the Wiley OR Encyclopedia

    Verbal Description:

    Remarks: This is an introductory encyclopedia article on various variants of Brownian Motion.

  13. 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.

    Remarks:

  14. 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.

    Remarks:

  15. 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.

    Remarks:

  16. 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.

  17. 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.

  18. 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

  19. 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

  20. 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.

    Remarks:

  21. 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.

    Remarks:

  22. 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.

  23. 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.

  24. 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.


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