On the spectral distribution of large weighted random regular graphs

McKay proved that the limiting spectral measures of the ensembles of $d$-regular graphs with $N$ vertices converge to Kesten's measure as $N\to\infty$. In this paper we explore the case of weighted graphs. More precisely, given a large $d$-regular graph we assign random weights, drawn from some distribution $\mathcal{W}$, to its edges. We study the relationship between $\mathcal{W}$ and the associated limiting spectral distribution obtained by averaging over the weighted graphs. Among other results, we establish the existence of a unique `eigendistribution', i.e., a weight distribution $\mathcal{W}$ such that the associated limiting spectral distribution is a rescaling of $\mathcal{W}$. Initial investigations suggested that the eigendistribution was the semi-circle distribution, which by Wigner's Law is the limiting spectral measure for real symmetric matrices. We prove this is not the case, though the deviation between the eigendistribution and the semi-circular density is small (the first seven moments agree, and the difference in each higher moment is $O(1/d^2)$). Our analysis uses combinatorial results about closed acyclic walks in large trees, which may be of independent interest.Comment: Version 1.0, 19 page

The Phase-I Trigger Readout Electronics Upgrade of the ATLAS Liquid Argon Calorimeters

The Phase-I trigger readout electronics upgrade of the ATLAS Liquid Argon calorimeters enhances the physics reach of the experiment during the upcoming operation at increasing Large Hadron Collider luminosities. The new system, installed during the second Large Hadron Collider Long Shutdown, increases the trigger readout granularity by up to a factor of ten as well as its precision and range. Consequently, the background rejection at trigger level is improved through enhanced filtering algorithms utilizing the additional information for topological discrimination of electromagnetic and hadronic shower shapes. This paper presents the final designs of the new electronic elements, their custom electronic devices, the procedures used to validate their proper functioning, and the performance achieved during the commissioning of this system.Comment: 56 pages, 41 figures, 6 table

The Phase-I trigger readout electronics upgrade of the ATLAS Liquid Argon calorimeters

International audienceThe Phase-I trigger readout electronics upgrade of the ATLAS Liquid Argon calorimeters enhances the physics reach of the experiment during the upcoming operation at increasing Large Hadron Collider luminosities. The new system, installed during the second Large Hadron Collider Long Shutdown, increases the trigger readout granularity by up to a factor of ten as well as its precision and range. Consequently, the background rejection at trigger level is improved through enhanced filtering algorithms utilizing the additional information for topological discrimination of electromagnetic and hadronic shower shapes. This paper presents the final designs of the new electronic elements, their custom electronic devices, the procedures used to validate their proper functioning, and the performance achieved during the commissioning of this system

The Phase-I Trigger Readout Electronics Upgrade of the ATLAS Liquid Argon Calorimeters

The Phase-I trigger readout electronics upgrade of the ATLAS Liquid Argon calorimeters enhances the physics reach of the experiment during the upcoming operation at increasing Large Hadron Collider luminosities. The new system, installed during the second Large Hadron Collider Long Shutdown, increases the trigger readout granularity by up to a factor of ten as well as its precision and range. Consequently, the background rejection at trigger level is improved through enhanced filtering algorithms utilizing the additional information for topological discrimination of electromagnetic and hadronic shower shapes. This paper presents the final designs of the new electronic elements, their custom electronic devices, the procedures used to validate their proper functioning, and the performance achieved during the commissioning of this system

The ATLAS experiment at the CERN Large Hadron Collider: a description of the detector configuration for Run 3

Abstract The ATLAS detector is installed in its experimental cavern at Point 1 of the CERN Large Hadron Collider. During Run 2 of the LHC, a luminosity of  ℒ = 2 × 1034 cm-2 s-1 was routinely achieved at the start of fills, twice the design luminosity. For Run 3, accelerator improvements, notably luminosity levelling, allow sustained running at an instantaneous luminosity of  ℒ = 2 × 1034 cm-2 s-1, with an average of up to 60 interactions per bunch crossing. The ATLAS detector has been upgraded to recover Run 1 single-lepton trigger thresholds while operating comfortably under Run 3 sustained pileup conditions. A fourth pixel layer 3.3 cm from the beam axis was added before Run 2 to improve vertex reconstruction and b-tagging performance. New Liquid Argon Calorimeter digital trigger electronics, with corresponding upgrades to the Trigger and Data Acquisition system, take advantage of a factor of 10 finer granularity to improve triggering on electrons, photons, taus, and hadronic signatures through increased pileup rejection. The inner muon endcap wheels were replaced by New Small Wheels with Micromegas and small-strip Thin Gap Chamber detectors, providing both precision tracking and Level-1 Muon trigger functionality. Trigger coverage of the inner barrel muon layer near one endcap region was augmented with modules integrating new thin-gap resistive plate chambers and smaller-diameter drift-tube chambers. Tile Calorimeter scintillation counters were added to improve electron energy resolution and background rejection. Upgrades to Minimum Bias Trigger Scintillators and Forward Detectors improve luminosity monitoring and enable total proton-proton cross section, diffractive physics, and heavy ion measurements. These upgrades are all compatible with operation in the much harsher environment anticipated after the High-Luminosity upgrade of the LHC and are the first steps towards preparing ATLAS for the High-Luminosity upgrade of the LHC. This paper describes the Run 3 configuration of the ATLAS detector.</jats:p

The ATLAS experiment at the CERN Large Hadron Collider: a description of the detector configuration for Run 3

The ATLAS detector is installed in its experimental cavern at Point 1 of the CERN Large Hadron Collider. During Run 2 of the LHC, a luminosity of ℒ = 2 × 1034 cm-2 s-1 was routinely achieved at the start of fills, twice the design luminosity. For Run 3, accelerator improvements, notably luminosity levelling, allow sustained running at an instantaneous luminosity of ℒ = 2 × 1034 cm-2 s-1, with an average of up to 60 interactions per bunch crossing. The ATLAS detector has been upgraded to recover Run 1 single-lepton trigger thresholds while operating comfortably under Run 3 sustained pileup conditions. A fourth pixel layer 3.3 cm from the beam axis was added before Run 2 to improve vertex reconstruction and b-tagging performance. New Liquid Argon Calorimeter digital trigger electronics, with corresponding upgrades to the Trigger and Data Acquisition system, take advantage of a factor of 10 finer granularity to improve triggering on electrons, photons, taus, and hadronic signatures through increased pileup rejection. The inner muon endcap wheels were replaced by New Small Wheels with Micromegas and small-strip Thin Gap Chamber detectors, providing both precision tracking and Level-1 Muon trigger functionality. Trigger coverage of the inner barrel muon layer near one endcap region was augmented with modules integrating new thin-gap resistive plate chambers and smaller-diameter drift-tube chambers. Tile Calorimeter scintillation counters were added to improve electron energy resolution and background rejection. Upgrades to Minimum Bias Trigger Scintillators and Forward Detectors improve luminosity monitoring and enable total proton-proton cross section, diffractive physics, and heavy ion measurements. These upgrades are all compatible with operation in the much harsher environment anticipated after the High-Luminosity upgrade of the LHC and are the first steps towards preparing ATLAS for the High-Luminosity upgrade of the LHC. This paper describes the Run 3 configuration of the ATLAS detector

The ATLAS experiment at the CERN Large Hadron Collider: a description of the detector configuration for Run 3

Abstract The ATLAS detector is installed in its experimental cavern at Point 1 of the CERN Large Hadron Collider. During Run 2 of the LHC, a luminosity of  ℒ = 2 × 1034 cm-2 s-1 was routinely achieved at the start of fills, twice the design luminosity. For Run 3, accelerator improvements, notably luminosity levelling, allow sustained running at an instantaneous luminosity of  ℒ = 2 × 1034 cm-2 s-1, with an average of up to 60 interactions per bunch crossing. The ATLAS detector has been upgraded to recover Run 1 single-lepton trigger thresholds while operating comfortably under Run 3 sustained pileup conditions. A fourth pixel layer 3.3 cm from the beam axis was added before Run 2 to improve vertex reconstruction and b-tagging performance. New Liquid Argon Calorimeter digital trigger electronics, with corresponding upgrades to the Trigger and Data Acquisition system, take advantage of a factor of 10 finer granularity to improve triggering on electrons, photons, taus, and hadronic signatures through increased pileup rejection. The inner muon endcap wheels were replaced by New Small Wheels with Micromegas and small-strip Thin Gap Chamber detectors, providing both precision tracking and Level-1 Muon trigger functionality. Trigger coverage of the inner barrel muon layer near one endcap region was augmented with modules integrating new thin-gap resistive plate chambers and smaller-diameter drift-tube chambers. Tile Calorimeter scintillation counters were added to improve electron energy resolution and background rejection. Upgrades to Minimum Bias Trigger Scintillators and Forward Detectors improve luminosity monitoring and enable total proton-proton cross section, diffractive physics, and heavy ion measurements. These upgrades are all compatible with operation in the much harsher environment anticipated after the High-Luminosity upgrade of the LHC and are the first steps towards preparing ATLAS for the High-Luminosity upgrade of the LHC. This paper describes the Run 3 configuration of the ATLAS detector.</jats:p