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Clique packings in random graphs
Simon Griffiths, Let\'icia Mattos
https://arxiv.org/abs/2405.00667 https://arxiv.org/pdf/2405.00…

Clique packings in random graphs
We consider the question of how many edge-disjoint near-maximal cliques may be found in the dense Erdős-Rényi random graph $G(n,p)$. Recently Acan and Kahn showed that the largest such family contains only $O(n^2/(\log{n})^3)$ cliques, with high probability, which disproved a conjecture of Alon and Spencer. We prove the corresponding lower bound, $Ω(n^2/(\log{n})^3)$, by considering a random graph process which sequentially selects and deletes near-maximal cliques. To analyse this process we…

This https://arxiv.org/abs/2303.02274 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A "lifting" method for exponential large deviation estimates and an application to certain non-stationary 1D lattice Anderson models
Proofs of localization for random Schrödinger operators with sufficiently regular distribution of the potential can take advantage of the fractional moment method introduced by Aizenman-Molchanov, or use the classical Wegner estimate as part of another method, e.g. the multi-scale analysis introduced by Fröhlich-Spencer and significantly developed by Klein and his collaborators. When the potential distribution is singular, most proofs rely crucially on exponential estimates of events correspo…

Direct Experimental Constraints on the Spatial Extent of a Neutrino Wavepacket
Joseph Smolsky, Kyle G Leach, Ryan Abells, Pedro Amaro, Adrien Andoche, Keith Borbridge, Connor Bray, Robin Cantor, David Diercks, Spencer Fretwell, Stephan Friedrich, Abigail Gillespie, Mauro Guerra, Ad Hall, Cameron N Harris, Jackson T Harris, Calvin Hinkle, Amii Lamm, Leendert M Hayen, Paul-Antoine Hervieux, Geon-Bo Kim, Inwook Kim, Annika Lennarz, Vincenzo Lordi, Jorge Machado, Andrew Marino, David McKee…

Direct Experimental Constraints on the Spatial Extent of a Neutrino Wavepacket
Despite their high relative abundance in our Universe, neutrinos are the least understood fundamental particles of nature. They also provide a unique system to study quantum coherence in fundamental systems due to their extremely weak interaction probabilities. The quantum properties of neutrinos emitted in experimentally relevant sources are virtually unknown and theoretical predictions for the spatial width of neutrino wavepackets vary by many orders of magnitude. In weak nuclear decay, the s…