Divisibility and primality in random walks

In this paper we study the divisibility and primality properties of the Bernoulli random walk. We improve or extend some of our divisibility results to wide classes of iid or independent non iid random walks. We also obtain new primality results for the Rademacher random walk. We study the value distribution of divisors of the random walk in the Cram\'er model, and obtain a general estimate of a similar kind to that of the Bernouilli model. Earlier results on divisors and quasi-prime numbers in the Bernoulli model are recorded, as well as some other recent for the Cram\'er random model, based on an estimate due to Selberg.Comment: 38 page

On Mukhin's necessary and sufficient condition for the validity of the local limit theorem

Mukhin found in 1984 an important necessary and sufficient condition for the validity of the local limit theorem. Revisiting the succint proof given in \cite{Mu2}, we could only prove rigorously a weaker necessary and sufficient condition, with a significantly different formulation. This is the object of this short Note.Comment: 4 pages. arXiv admin note: substantial text overlap with arXiv:2208.0270

Deep Neural Networks for Energy and Position Reconstruction in EXO-200

We apply deep neural networks (DNN) to data from the EXO-200 experiment. In the studied cases, the DNN is able to reconstruct the relevant parameters - total energy and position - directly from raw digitized waveforms, with minimal exceptions. For the first time, the developed algorithms are evaluated on real detector calibration data. The accuracy of reconstruction either reaches or exceeds what was achieved by the conventional approaches developed by EXO-200 over the course of the experiment. Most existing DNN approaches to event reconstruction and classification in particle physics are trained on Monte Carlo simulated events. Such algorithms are inherently limited by the accuracy of the simulation. We describe a unique approach that, in an experiment such as EXO-200, allows to successfully perform certain reconstruction and analysis tasks by training the network on waveforms from experimental data, either reducing or eliminating the reliance on the Monte Carlo.Comment: Accepted version. 33 pages, 28 figure

Search for nucleon decays with EXO-200

A search for instability of nucleons bound in $^{136}$Xe nuclei is reported with 223 kg$\cdot$yr exposure of $^{136}$Xe in the EXO-200 experiment. Lifetime limits of 3.3$\times 10^{23}$ and 1.9$\times 10^{23}$ yrs are established for nucleon decay to $^{133}$Sb and $^{133}$Te, respectively. These are the most stringent to date, exceeding the prior decay limits by a factor of 9 and 7, respectively

Measurement of the Spectral Shape of the beta-decay of 137Xe to the Ground State of 137Cs in EXO-200 and Comparison with Theory

We report on a comparison between the theoretically predicted and experimentally measured spectra of the first-forbidden non-unique $\beta$-decay transition ^{137}\textrm{Xe}(7/2^-)\to\,^{137}\textrm{Cs}(7/2^+). The experimental data were acquired by the EXO-200 experiment during a deployment of an AmBe neutron source. The ultra-low background environment of EXO-200, together with dedicated source deployment and analysis procedures, allowed for collection of a pure sample of the decays, with an estimated signal-to-background ratio of more than 99-to-1 in the energy range from 1075 to 4175 keV. In addition to providing a rare and accurate measurement of the first-forbidden non-unique $\beta$-decay shape, this work constitutes a novel test of the calculated electron spectral shapes in the context of the reactor antineutrino anomaly and spectral bump.Comment: Version as accepted by PR

Sensitivity and discovery potential of the proposed nEXO experiment to neutrinoless double beta decay

The next-generation Enriched Xenon Observatory (nEXO) is a proposed experiment to search for neutrinoless double beta ($0\nu\beta\beta$) decay in $^{136}$Xe with a target half-life sensitivity of approximately $10^{28}$ years using $5\times10^3$ kg of isotopically enriched liquid-xenon in a time projection chamber. This improvement of two orders of magnitude in sensitivity over current limits is obtained by a significant increase of the $^{136}$Xe mass, the monolithic and homogeneous configuration of the active medium, and the multi-parameter measurements of the interactions enabled by the time projection chamber. The detector concept and anticipated performance are presented based upon demonstrated realizable background rates.Comment: v2 as publishe