Novel scaling limits for critical inhomogeneous random graphs (2009)
Bhamidi, Shankar, Van Der Hofstad, Remco
We find scaling limits for the sizes of the largest components at criticality for the rank-1 inhomogeneous random graphs with power-law degrees with exponent $\tau$. We investigate the case where...
Scaling limits for critical inhomogeneous random graphs with finite third moments (2009)
Bhamidi, Shankar, Van Der Hofstad, Remco, Van Leeuwaarden, Johan
We identify the scaling limits for the sizes of the largest components at criticality for inhomogeneous random graphs when the degree exponent $\tau$ satisfies $\tau>4$. We see that the sizes of the...
Extreme value theory, Poisson-Dirichlet distributions and FPP on random networks (2009)
Bhamidi, Shankar, Van Der Hofstad, Remco, Hooghiemstra, Gerard
We study first passage percolation on the configuration model (CM) having power-law degrees with exponent $\tau\in [1,2)$. To this end we equip the edges with exponential weights. We derive the...
Spectra of large random trees (2009)
Bhamidi, Shankar, Evans, Steven N., Sen, Arnab
We analyze the eigenvalues of the adjacency matrices of a wide variety of random trees. Using general, broadly applicable arguments based on the interlacing inequalities for the eigenvalues of a...
Mixing time of exponential random graphs (2008)
Bhamidi, Shankar, Bresler, Guy, Sly, Allan
Exponential random graphs are used extensively in the sociology literature. This model seeks to incorporate in random graphs the notion of reciprocity, that is, the larger than expected number of...
IMS Lecture Notes–Monograph Series (2008)
Shankar Bhamidi, Steven N. Evans, Ron Peled, Peter Ralph
Brownian motion on time scales, basic hypergeometric functions, and some continued fractions of Ramanujan
IMS Lecture Notes–Monograph Series (2008)
Shankar Bhamidi, Steven N. Evans, Ron Peled, Peter Ralph
Brownian motion on disconnected sets, basic hypergeometric functions, and some continued fractions of Ramanujan
Spectra of Random trees (2008)
Shankar Bhamidi, Steve Evans, Arnab Sen
We analyze the spectral distribution of the adjacency matrix and the graph Laplacian for a wide variety of random trees. Using soft arguments which seem to be applicable in a wide variety of...
Mixing time of exponential random graphs (2008)
Shankar Bhamidi, Guy Bresler, Allan Sly
A plethora of random graph models have been developed in recent years to study a range of problems on networks, driven by the wide availability of data from many social, telecommunication,...
Edge Flows in the Complete Random-Lengths Network (2007)
Aldous, David J., Bhamidi, Shankar
Consider the complete n-vertex graph whose edge-lengths are independent exponentially distributed random variables. Simultaneously for each pair of vertices, put a constant flow between them along...
First Passage percolation on locally tree like networks I: Dense random graphs (2007)
We study various properties of least cost paths under iid disorder for the complete graph and dense Erdos-Renyii random graphs in the connected phase, with iid exponential and uniform weights on...
Universal techniques to analyze preferential attachment trees: Global and Local analysis (2007)
We use embeddings in continuous time Branching processes to derive asymptotics for various statistics associated with different models of preferential attachment. This powerful method allows us to...
Edge Flows in the Complete Random-Lengths Network. eprint arXiv: 0708.0555 (2007)
David J. Aldous, Shankar Bhamidi
Consider the complete n-vertex graph whose edge-lengths are independent exponentially distributed random variables. Simultaneously for each pair of vertices, put a constant flow between them along...
Network Delay Inference from Additive Metrics (2006)
Bhamidi, Shankar, Rajagopal, Ram, Roch, Sebastien
We demonstrate the use of computational phylogenetic techniques to solve a central problem in inferential network monitoring. More precisely, we design a novel algorithm for multicast-based delay...
Shankar Bhamidi, Sébastien Roch, Ram Rajagopal
We demonstrate the use of computational phylogenetic techniques to solve a central problem in inferential network monitoring. More precisely, we design a novel algorithm for multicast-based delay...
Bhamidi, Shankar, Evans, Steven N., Peled, Ron, Ralph, Peter
Motivated by L\'{e}vy's characterization of Brownian motion on the line, we propose an analogue of Brownian motion that has as its state space an arbitrary closed subset of the line that is unbounded...