Anirban Basak

collaborators

4 papers

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

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.…