48 citations · 174 across the 18 of their papers we have counts for
18 papers · 1 filter
Geometry of critical discrete structures: long-range percolation on the hierarchical lattice and the discrete torus
Arghyadeep Chatterjee, Sourish Maniyar, Sanchayan Sen
Consider (a) balls of growing volumes in the -dimensional hierarchical lattice, and (b) the -dimensional discrete torus on vertices. Place edges…
Scaling limits and universality: Critical percolation on weighted graphs converging to an graphon
Jnaneshwar Baslingker, Shankar Bhamidi, Nicolas Broutin +2
We develop a general universality technique for establishing metric scaling limits of critical random discrete structures exhibiting mean-field behavior that requires four ingredie…
Geometry of the minimal spanning tree in the heavy-tailed regime: new universality classes
Shankar Bhamidi, Sanchayan Sen
A well-known open problem on the behavior of optimal paths in random graphs in the strong disorder regime, formulated by statistical physicists, and supported by a large amount of…
Global lower mass-bound for critical configuration models in the heavy-tailed regime
Shankar Bhamidi, Souvik Dhara, Remco van der Hofstad +1
We establish the global lower mass-bound property for the largest connected components in the critical window for the configuration model when the degree distribution has an infini…
On breadth-first constructions of scaling limits of random graphs and random unicellular maps
Grégory Miermont, Sanchayan Sen
We give alternate constructions of (i) the scaling limit of the uniform connected graphs with given fixed surplus, and (ii) the continuum random unicellular map (CRUM) of a given g…
Geometry of the minimal spanning tree of a random -regular graph
Louigi Addario-Berry, Sanchayan Sen
The global structure of the minimal spanning tree (MST) is expected to be universal for a large class of underlying random discrete structures. However, very little is known about…
A probabilistic approach to the leader problem in random graphs
Louigi Addario-Berry, Shankar Bhamidi, Sanchayan Sen
We study the fixation time of the identity of the leader, i.e., the most massive component, in the general setting of Aldous's multiplicative coalescent [4, 5], which in an asympto…
Universality for critical heavy-tailed network models: Metric structure of maximal components
Shankar Bhamidi, Souvik Dhara, Remco van der Hofstad +1
We study limits of the largest connected components (viewed as metric spaces) obtained by critical percolation on uniformly chosen graphs and configuration models with heavy-tailed…
Heavy-tailed configuration models at criticality
Souvik Dhara, Remco van der Hofstad, Johan S. H. van Leeuwaarden +1
We study the critical behavior of the component sizes for the configuration model when the tail of the degree distribution of a randomly chosen vertex is a regularly-varying functi…
Geometry of the vacant set left by random walk on random graphs, Wright's constants, and critical random graphs with prescribed degrees
Shankar Bhamidi, Sanchayan Sen
We provide an explicit algorithm for sampling a uniform simple connected random graph with a given degree sequence. By products of this central result include: (i) continuum scalin…
Critical window for the configuration model: finite third moment degrees
Souvik Dhara, Remco van der Hofstad, Johan S. H. van Leeuwaarden +1
We investigate the component sizes of the critical configuration model, as well as the related problem of critical percolation on a supercritical configuration model. We show that,…
The multiplicative coalescent, inhomogeneous continuum random trees, and new universality classes for critical random graphs
Shankar Bhamidi, Remco van der Hofstad, Sanchayan Sen
One major open conjecture in the area of critical random graphs, formulated by statistical physicists, and supported by a large amount of numerical evidence over the last decade [2…
Scaling limits of random graph models at criticality: Universality and the basin of attraction of the Erdős-Rényi random graph
Shankar Bhamidi, Nicolas Broutin, Sanchayan Sen +1
A wide array of random graph models have been postulated to understand properties of observed networks. Typically these models have a parameter and a critical time when a…
Continuum limit of critical inhomogeneous random graphs
Shankar Bhamidi, Sanchayan Sen, Xuan Wang
Motivated by applications, the last few years have witnessed tremendous interest in understanding the structure as well as the behavior of dynamics for inhomogeneous random graph m…
On the largest component in the subcritical regime of the Bohman-Frieze process
Sanchayan Sen
Kang, Perkins and Spencer showed that the size of the largest component of the Bohman-Frieze process at a fixed time smaller than , the critical time for the process is $L…
Minimal spanning trees and Stein's method
Sourav Chatterjee, Sanchayan Sen
Kesten and Lee [36] proved that the total length of a minimal spanning tree on certain random point configurations in satisfies a central limit theorem. They also ra…
The Speed of a Biased Walk on a Galton-Watson Tree without Leaves is Monotonic with Respect to Progeny Distributions for High Values of Bias
Behzad Mehrdad, Sanchayan Sen, Lingjiong Zhu
Consider biased random walks on two Galton-Watson trees without leaves having progeny distributions and (GW and GW) where and are supported on…
Limiting spectral distribution of sample autocovariance matrices
Anirban Basak, Arup Bose, Sanchayan Sen
We show that the empirical spectral distribution (ESD) of the sample autocovariance matrix (ACVM) converges as the dimension increases, when the time series is a linear process wit…