Fluctuations of Matrix Entries of Regular Functions of Wigner Matrices

We study the fluctuations of the matrix entries of regular functions of Wigner random matrices in the limit when the matrix size goes to infinity. In the case of the Gaussian ensembles (GOE and GUE) this problem was considered by A.Lytova and L.Pastur in J. Stat. Phys., v.134, 147-159 (2009). Our results are valid provided the off-diagonal matrix entries have finite fourth moment, the diagonal matrix entries have finite second moment, and the test functions have four continuous derivatives in a neighborhood of the support of the Wigner semicircle law.Comment: minor corrections; the manuscript will appear in the Journal of Statistical Physic

Energy Savings Opportunities and Energy Efficiency Performance Indicators for a Serial Production Line

Part 2: Sustainable Supply ChainsInternational audienceModern manufacturing facilities waste various energy savings opportunities (ESO) and lack proper performance indicators to measure energy efficiency on the production line. The ESO is an opportunity window calculated from on-line production data, such as production count, machine downtime records, buffer levels, and machine idle status, allowing certain machines to be turned off for energy savings without negatively affecting throughput. New energy efficiency performance indicators are presented that use real time production data to identify the least energy efficiency machine on the line. The energy savings opportunity strategy utilizes the Energy Efficiency Performance Indicators (EEPI) to take the opportunity window for the least energy efficient machine at opportune times, allowing for improvements to be made to the machine, increasing the overall energy efficiency of the line