6 papers
Independence of linear spectral statistics and the point process at the edge of Wigner matrices
Debapratim Banerjee
In the current paper we consider a Wigner matrix and consider an analytic function of polynomial growth on a set containing the support of the semicircular law in its interior. We…
Fluctuations of the free energy of the mixed -spin mean field spin glass model
Debapratim Banerjee, David Belius
We prove the convergence in distribution of the fluctuations of the free energy of the mixed -spin Sherrington-Kirkpatrick model with non-vanishing -spin component at high en…
A Bernstein type inequality for sums of selections from three dimensional arrays
Debapratim Banerjee, Matteo Sordello
We consider the three dimensional array , with , and the two random statistics $T_{1}:= \sum_{i=1}^n \sum_{j=1}…
Fluctuation of the free energy of Sherrington-Kirkpatrick model with Curie-Weiss interaction: the paramagnetic regime
Debapratim Banerjee
We consider a spin system with pure two spin Sherrington-Kirkpatrick Hamiltonian with Curie-Weiss interaction. The model where the spins are spherically symmetric was considered by…
High-dimensional CLT: Improvements, Non-uniform Extensions and Large Deviations
Arun Kumar Kuchibhotla, Somabha Mukherjee, Debapratim Banerjee
Central limit theorems (CLTs) for high-dimensional random vectors with dimension possibly growing with the sample size have received a lot of attention in the recent times. Chernoz…
Asymptotic normality and analysis of variance of log-likelihood ratios in spiked random matrix models
Debapratim Banerjee, Zongming Ma
The present manuscript studies signal detection by likelihood ratio tests in a number of spiked random matrix models, including but not limited to Gaussian mixtures and spiked Wish…