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 fantastic branch of mathematics called probability to tell me something truly useful about the real world. The crux of the problem almost always boils down to asking the "right questions'' at the right time.

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: Submitted to 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: Submitted to 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: Submitted to the Special Issue on Statistical Mechanics of Random Structures, Journal of Mathematical Physics .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: Working draft .pdf version
   
   Verbal Description:.pdf version.
   
   Remarks:
7. Title: Mixing time of exponential random graphs
   
   co-authors: Guy Bresler and Allan Sly
   
   Published: Submitted to FOCS 2008 .pdf version
   
   Verbal Description:.pdf version.
   
   Remarks:

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