COVARIANCE MATRICES

nTn where Xn = (Xij) is n × N with i.i.d. complex standardized entries having finite fourth moment, and T 1/2 n is a Hermitian square root of the nonnegative definite Hermitian matrix Tn.The limiting behavior, as n →∞with n/N approaching a positive constant, of functionals of the eigenvalues of Bn, where each is given equal weight, is studied. Due to the limiting behavior of the empirical spectral distribution of Bn, it is known that these linear spectral statistics converges a.s. to a nonrandom quantity. This paper shows their rate of convergence to be 1/n by proving, after proper scaling, that they form a tight sequence. Moreover, if EX2 11 = 0andE|X11 | 4 = 2, or if X11 and Tn are real and EX4 11 = 3, they are shown to have Gaussian limits. 1. Introduction. Due to the rapid development of modern technology, statisticians are confronted with the task of analyzing data with ever increasing dimension. For example, stock market analysis can now include a large numbe

The Trajectory of Revisional Bariatric Surgery: Open to Laparoscopic to Robotic

Metabolic and bariatric surgery (MBS) is the most effective therapeutic intervention for patients with obesity, with sleeve gastrectomy (SG) being the most commonly performed primary MBS procedure. Long-term studies have demonstrated that 15–20% of patients require revisional bariatric surgery (RBS) due to weight-related issues or surgical complications. Despite the gold standard being laparoscopic revision, there are other available approaches such as open or robotic-assisted. An extensive literature review was performed for articles from their inception to February 2024. A descriptive review of MBS procedures (SG, Roux-en-Y gastric bypass (RYGB), single anastomosis duodeno-ileostomy (SADI) and biliopancreatic diversion-duodenal switch (BPD-DS)) was carried out to report and compare outcomes between primary and revisional bariatric surgery. A similar review was conducted to compare outcomes of revisional approaches (open, laparoscopic, robotic). RYGB remains the dominant RBS with a similar safety profile compared to revisional SADI and BPD-DS. In terms of the RBS surgical approach, all three options showed comparable short and long-term outcomes, with robotic RBS being associated with longer operative time and variable length of stay. Additional long-term studies are required to further validate our conclusions