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Abstract We revisit the question addressed in recent papers by Garriga et al.: what determines the rest frame of pair nucleation in a constant electric field? The conclusion reached in these papers is that pairs are observed to nucleate at rest in the rest frame of the detector which is used to detect the pairs. A similar conclusion should apply to bubble nucleation in a false vacuum. This conclusion however is subject to doubt due to the unphysical nature of the model of a constant eternal electric field that was used by Garriga et al. The number density of pairs in such a field would be infinite at any finite time. Here we address the same question in a more realistic model where the electric field is turned on at a finite timet₀in the past. The process of turning on the field breaks the Lorentz invariance of the model and could in principle influence the frame of pair nucleation. We find however that the conclusion of Garriga et al. still holds in the limitt₀ → -∞. This shows that the setup process of the electric field does not have a lasting effect on the observed rest frame of pair nucleation. On the other hand, the electric current and charge density due to the pairs are determined by the way in which the electric field was turned on. 

Abstract Analysis of non-probability survey samples requires auxiliary information at the population level. Such information may also be obtained from an existing probability survey sample from the same finite population. Mass imputation has been used in practice for combining non-probability and probability survey samples and making inferences on the parameters of interest using the information collected only in the non-probability sample for the study variables. Under the assumption that the conditional mean function from the non-probability sample can be transported to the probability sample, we establish the consistency of the mass imputation estimator and derive its asymptotic variance formula. Variance estimators are developed using either linearization or bootstrap. Finite sample performances of the mass imputation estimator are investigated through simulation studies. We also address important practical issues of the method through the analysis of a real-world non-probability survey sample collected by the Pew Research Centre.