7 papers
Central Limit Theorem in High Dimensions : The Optimal Bound on Dimension Growth Rate
Debraj Das, Soumendra Lahiri
In this article, we try to give an answer to the simple question: ``\textit{What is the critical growth rate of the dimension as a function of the sample size for which the…
Higher Order Refinements by Bootstrap in Lasso and other Penalized Regression Methods
Debraj Das, Arindam Chatterjee, S. N. Lahiri
Selection of important covariates and to drop the unimportant ones from a high-dimensional regression model is a long standing problem and hence have received lots of attention in…
Critical exponents in mean-field classical spin systems
Yoshiyuki Y. Yamaguchi, Debraj Das, Shamik Gupta
For a mean-field classical spin system exhibiting a second-order phase transition in the stationary state, we obtain within the corresponding phase space evolution according to the…
Relaxation to equilibrium in models of classical spins with long-range interactions
Debraj Das, Shamik Gupta
For a model long-range interacting system of classical Heisenberg spins, we study how fluctuations, such as those arising from having a finite system size or through interaction wi…
Reconstructing bifurcation behavior of a nonlinear dynamical system by introducing weak noise
Debraj Das, Sayan Roy, Shamik Gupta
For a model nonlinear dynamical system, we show how one may obtain its bifurcation behavior by introducing noise into the dynamics and then studying the resulting Langevin dynamics…
Exact correlations in the nonequilibrium stationary state of the noisy Kuramoto model
Debraj Das, Shamik Gupta
We obtain exact results on autocorrelation of the order parameter in the nonequilibrium stationary state of a paradigmatic model of spontaneous collective synchronization, the Kura…