Gibbs random fields with unbounded spins on unbounded degree graphs

Gibbs random fields corresponding to systems of real-valued spins (e.g. systems of interacting anharmonic oscillators) indexed by the vertices of unbounded degree graphs with a certain summability property are constructed. It is proven that the set of tempered Gibbs random fields is non-void and weakly compact, and that they obey uniform exponential integrability estimates. In the second part of the paper, a class of graphs is described in which the mentioned summability is obtained as a consequence of a property, by virtue of which vertices of large degree are located at large distances from each other. The latter is a stronger version of a metric property, introduced in [Bassalygo, L. A. and Dobrushin, R. L. (1986). \textrm{Uniqueness of a Gibbs field with a random potential--an elementary approach.}\textit{Theory Probab. Appl.} {\bf 31} 572--589]

Performance of Calorimetry in ALICE

The ALICE experiment at LHC studies the strong interaction sector of the Standard Model with pp, pA and AA collisions. Within the scope of the physics program, measurements of photons, neutral mesons and jets in ALICE are performed by two electromagnetic calorimeters. Precise and high-granularity photon spectrometer (PHOS) composed of lead-tungstate crystals, along with a wide-aperture lead-scintillator sampling calorimeter (EMCal) provide complementary measurements of photon observables in a wide kinematic range. The calorimeter trigger system allows the experiment to utilize efficiently the full delivered luminosity, recording a data sample enhanced with high-energy photons and jets. Performance of the ALICE calorimeters from proton-proton to heavy-ion collision systems is discussed and illustrated by physics results derived from data collected by ALICE with its electromagnetic calorimeter system.Comment: 7 pages, 5 figures. Sixth Annual Conference on Large Hadron Collider Physics (LHCP2018), 4-9 June 2018, Bologna, Ital