Uniform point variance bounds in classical beta ensembles

In this paper, we give bounds on the variance of the number of points of the Circular and the Gaussian [Formula: see text] Ensemble in arcs of the unit circle or intervals of the real line. These bounds are logarithmic with respect to the renormalized length of these sets, which is expected to be optimal up to a multiplicative constant depending only on [Formula: see text].

Variance constrained trajectory tracking for tandem-rotor helicopters

Purpose This paper aims to present novel results for trajectory tracking of tandem-rotor helicopters via variance-constrained controllers. Design/methodology/approach Regarding these purposes, linearized tandem-rotor helicopter models are benefitted. Findings Variance-constrained controllers are very beneficial for trajectory tracking of tandem-rotor helicopters while there exists variance bounds on outputs of interest. Practical implications Variance-constrained controllers can be used for cheaper tandem-rotor helicopter operations with high trajectory tracking quality. Originality/value Applying variance-constrained control strategy for tandem-rotor helicopters during trajectory tracking. This also causes less fuel consumption and green environment, and good trajectory tracking quality.