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Optimal decay of eigenvector overlap for non-Hermitian random matrices
No full textWe consider the standard overlap (math formular) of any bi-orthogonal family of left and right eigenvectors of a large random matrix X with centred i.i.d. entries and we prove that it decays as an inverse second power of the distance between the corresponding eigenvalues. This extends similar results for the complex Gaussian ensemble from Bourgade and Dubach [15], as well as Benaych-Georges and Zeitouni [13], to any i.i.d. matrix ensemble in both symmetry classes. As a main tool, we prove a two-resolvent local law for the Hermitisation of X uniformly in the spectrum with optimal decay rate and optimal dependence on the density near the spectral edge
A dense web of neutral gas in a galaxy proto-cluster post-reionization
No full textGalaxy clusters are the most massive, gravitationally bound structures in the Universe. They emerged through hierarchical structure formation of large-scale dark matter and baryon overdensities. Early galaxy ‘proto-clusters’ are believed to have substantially contributed to the cosmic star-formation rate density and served as ‘hotspots’ for the reionization of the intergalactic medium. Our understanding of the formation of these structures at the earliest cosmic epochs is, however, limited to sparse observations of their galaxy members or is based on phenomenological models and cosmological simulations. Here we report the detection of a large and coherent structure of neutral atomic hydrogen gas (H i) extending from a galaxy proto-cluster at redshift z = 5.4, one billion years after the Big Bang. The presence of this H i gas is revealed by strong damped Lyman-α absorption features observed in several background-galaxy spectra. Although the sight lines overall probe a large range in H i column densities, NHI = 1020 cm−2 to 1023.5 cm−2, they are similar across nearby sight lines, demonstrating that they probe the same dense neutral gas. This observation of a dense large-scale overdensity of cold neutral gas challenges current cosmological simulations and has strong implications for the reionization topology of the Universe