Anirban Basak

activity

20102026

most citedBalanced random Toeplitz and Hankel Matrices

15 citations · 35 across the 16 of their papers we have counts for

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24 papers · 1 filter

math.PR2026

Upper tail large deviations of regular subgraph counts in sparse random regular graphs

Anirban Basak, Shaibal Karmakar

For a $Δ$ -regular connected graph $H$ we obtain the upper tail large deviations speed and rate function for the number of copies of $H$ in $G_{n}^{d}$ , a random $d$ -regular gr…

math.PR2025

Spectral properties of random perturbations of non-normal Toeplitz matrices

Anirban Basak

Spectral properties of Toeplitz operators and their finite truncations have long been central in operator theory. In the finite dimensional, non-normal setting, the spectrum is not…

math.PR2025

Upper tail bounds for irregular graphs

Anirban Basak, Shaibal Karmakar

We consider the upper tail large deviations of subgraph counts for irregular graphs $H$ in $G (n, p)$ , the sparse Erdős-Rényi graph on $n$ vertices with edge connec…

math.PR2023

Potts and random cluster measures on locally regular-tree-like graphs

Anirban Basak, Amir Dembo, Allan Sly

Fixing $β \geq 0$ and an integer $q \geq 2$ , consider the ferromagnetic $q$ -Potts measures $μ_{n}^{β, B}$ on finite graphs $G_{n}$ on $n$ vertices, with external field strength $B \g…

math.PR2023

Large deviations of the largest eigenvalue of supercritical sparse Wigner matrices

Fanny Augeri, Anirban Basak

Consider a random symmetric matrix with i.i.d.~entries on and above its diagonal that are products of Bernoulli random variables and random variables with sub-Gaussian tails. Such…

math.PR2021

Upper tail of the spectral radius of sparse Erdős-Rényi graphs

Anirban Basak

We consider an Erdős-Rényi graph $G (n, p)$ on $n$ vertices with edge probability $p$ such that \[ \sqrt{\frac{\log n}{\log \log n}} \ll np \le n^{1/2-o(1)}, \label{eq:abs}…

math.PR2019

Upper tail large deviations of regular subgraph counts in Erdős-Rényi graphs in the full localized regime

Anirban Basak, Riddhipratim Basu

For a $Δ$ -regular connected graph $H$ the problem of determining the upper tail large deviation for the number of copies of $H$ in $G (n, p)$ , an Erdős-Rényi gra…

math.PR2019

Outliers of random perturbations of Toeplitz matrices with finite symbols

Anirban Basak, Ofer Zeitouni

Consider an $N \times N$ Toeplitz matrix $T_{N}$ with symbol $a (λ) := \sum_{ℓ = - d_{2}}^{d_{1}} a_{ℓ} λ^{ℓ}$ , perturbed by an additive noise matrix $N^{- γ} E_{N}$ , where the entries o…

math.PR2018

Spectrum of random perturbations of Toeplitz matrices with finite symbols

Anirban Basak, Elliot Paquette, Ofer Zeitouni

Let $T_{N}$ denote an $N \times N$ Toeplitz matrix with finite, $N$ independent symbol $a$ . For $E_{N}$ a noise matrix satisfying mild assumptions (ensuring, in particular, that $…

math.PR2018★ 1 cited

Sharp transition of the invertibility of the adjacency matrices of sparse random graphs

Anirban Basak, Mark Rudelson

We consider three different models of sparse random graphs:~undirected and directed Erdős-Rényi graphs, and random bipartite graph with an equal number of left and right vertices.…

math.PR2017

Regularization of non-normal matrices by Gaussian noise - the banded Toeplitz and twisted Toeplitz cases

Anirban Basak, Elliot Paquette, Ofer Zeitouni

We consider the spectrum of additive, polynomially vanishing random perturbations of deterministic matrices, as follows. Let $M_{N}$ be a deterministic $N \times N$ matrix, and let $G…

math.PR2017

The circular law for sparse non-Hermitian matrices

Anirban Basak, Mark Rudelson

For a class of sparse random matrices of the form $A_{n} = (ξ_{i, j} δ_{i, j})_{i, j = 1}^{n}$ , where ${ξ_{i, j}}$ are i.i.d.~centered sub-Gaussian random variables of unit variance, and $\{…

math.PR2017

Circular law for the sum of random permutation matrices

Anirban Basak, Nicholas Cook, Ofer Zeitouni

Let $P_{n}^{1}, \dots, P_{n}^{d}$ be $n \times n$ permutation matrices drawn independently and uniformly at random, and set $S_{n}^{d} := \sum_{ℓ = 1}^{d} P_{n}^{ℓ}$ . We show that if $\log^{12}n/(\l…

math.PR2017

Diffusion limit for the partner model at the critical value

Anirban Basak, Rick Durrett, Eric Foxall

The partner model is an SIS epidemic in a population with random formation and dissolution of partnerships, and with disease transmission only occuring within partnerships. Foxall,…

math.PR2016★ 5 cited

Large subgraphs in pseudo-random graphs

Anirban Basak, Shankar Bhamidi, Suman Chakraborty +1

We consider classes of pseudo-random graphs on $n$ vertices for which the degree of every vertex and the co-degree between every pair of vertices are in the intervals $(np - Cn^δ,n…

math.PR2015★ 3 cited

The Evolving Voter Model on Thick Graphs

Anirban Basak, Rick Durrett, Yuan Zhang

In the evolving voter model, when an individual interacts with a neighbor having an opinion different from theirs, they will with probability $1 - α$ imitate the neighbor but with pr…

math.PR2015

Universality of the mean-field for the Potts model

Anirban Basak, Sumit Mukherjee

We consider the Potts model with $q$ colors on a sequence of weighted graphs with adjacency matrices $A_{n}$ , allowing for both positive and negative weights. Under a mild regularity…

math.PR2015

Invertibility of Sparse non-Hermitian matrices

Anirban Basak, Mark Rudelson

We consider a class of sparse random matrices of the form $A_{n} = (ξ_{i, j} δ_{i, j})_{i, j = 1}^{n}$ , where ${ξ_{i, j}}$ are i.i.d.~centered random variables, and ${δ_{i, j}}$ are i.i.d.~…

math.PR2014

Limiting spectral distribution of a class of Hankel type random matrices

Anirban Basak, Arup Bose, Soumendu Sundar Mukherjee

We consider an indexed class of real symmetric random matrices which generalize the symmetric Hankel and Reverse Circulant matrices. We show that the limiting spectral distribution…

math.PR2014

Regularization of non-normal matrices by Gaussian noise

Ohad Feldheim, Elliot Paquette, Ofer Zeitouni

We consider the regularization of matrices $M^{N}$ written in Jordan form by additive Gaussian noise $N^{- γ} G^{N}$ , where $G^{N}$ is a matrix of i.i.d. standard Gaussians and $γ > 1/2$ so…

math.PR2012

Limiting Spectral Distribution of Sum of Unitary and Orthogonal Matrices

Anirban Basak, Amir Dembo

We show that the empirical eigenvalue measure for sum of $d$ independent Haar distributed $n$ -dimensional unitary matrices, converge for $n \to \infty$ to the Brown measure of the…

math.PR2012

Ferromagnetic Ising Measures on Large Locally Tree-Like Graphs

Anirban Basak, Amir Dembo

We consider the ferromagnetic Ising model on a sequence of graphs $G_{n}$ converging locally weakly to a rooted random tree. Generalizing [Montanari, Mossel, Sly '11], under an appro…

math.PR2011★ 8 cited

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…

math.PR2010★ 15 cited

Balanced random Toeplitz and Hankel Matrices

Anirban Basak, Arup Bose

Except the Toeplitz and Hankel matrices, the common patterned matrices for which the limiting spectral distribution (LSD) are known to exist, share a common property--the number of…