Electromagnetic and gravitational radiation from the coherent oscillation of electron-positron pairs and fields

Integrating equations of particle-number and energy-momentum conservation and Maxwell field equations, we study the oscillation and drift of electron and positron pairs coherently with fields after these pairs are produced in external electromagnetic fields. From the electric current of oscillating pairs, we obtain the energy spectrum of electromagnetic dipole radiation. This narrow spectrum is so peculiar that the detection of such radiation can identify pair production and oscillation in strong laser fields. We also obtain the energy spectrum of gravitational quadrapole radiation from the energy-momentum tensor of oscillating pairs and fields. Thus, we discuss the generation of gravitational waves on the basis of rapid development of strong laser fields.Comment: 6 pages, 4 figure

On Gaussian Comparison Inequality and Its Application to Spectral Analysis of Large Random Matrices

Recently, Chernozhukov, Chetverikov, and Kato [Ann. Statist. 42 (2014) 1564--1597] developed a new Gaussian comparison inequality for approximating the suprema of empirical processes. This paper exploits this technique to devise sharp inference on spectra of large random matrices. In particular, we show that two long-standing problems in random matrix theory can be solved: (i) simple bootstrap inference on sample eigenvalues when true eigenvalues are tied; (ii) conducting two-sample Roy's covariance test in high dimensions. To establish the asymptotic results, a generalized $\epsilon$-net argument regarding the matrix rescaled spectral norm and several new empirical process bounds are developed and of independent interest.Comment: to appear in Bernoull