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.

Papers

1. 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.
   
   
2. 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.
   
   
3. 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.
   
   
4. 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.
   
   
5. 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: This is the first part of two papers exploring how edge weights change the geometry of the shortest paths on networks.
   
   
6. 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:
7. 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
   
   
8. 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
   
   
9. 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.
   
   
10. 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.
    
    
11. 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:
    
    
12. 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:
    
    
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: 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.
    
    
15. Title: First Passage Percolation on Erdos-Renyi random graphs
    
    co-authors: Remco van der Hofstad and Gerard Hooghiemstra
    
    Published: Accepted in Combinatorics, Computing and Probability .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.
    
    
16. 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 modulo revision .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.
    
    
17. Title: Bohman-Frieze processes at criticality and emergence of the giant component
    
    co-authors: Amarjit Budhiraja and Xuan Wang
    
    Published: Submitted to the Annals of Probability .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.
    
    

Works in Progress

The following describes work still in progress. They are all still in the nascent stage.

1. Title: Phase transitions and Network tomography
   
   Co-author: Sebastien Roch
   
   
2. Title: Universality for some combinatorial optimization models
   
   Co-author: Sourav Chatterjee
   
   
3. Title: First Passage percolation on random networks and universality of hopcount.
   
   
4. Title: Viral Marketing and Statistical Physics
   
   Co-author:Allan Sly