scholarly journals Basic Properties of Strong Mixing Conditions. A Survey and Some Open Questions

2005 ◽  
Vol 2 (0) ◽  
pp. 107-144 ◽  
Author(s):  
Richard C. Bradley
2012 ◽  
Vol 12 (01) ◽  
pp. 1150004
Author(s):  
RICHARD C. BRADLEY

In an earlier paper by the author, as part of a construction of a counterexample to the central limit theorem under certain strong mixing conditions, a formula is given that shows, for strictly stationary sequences with mean zero and finite second moments and a continuous spectral density function, how that spectral density function changes if the observations in that strictly stationary sequence are "randomly spread out" in a particular way, with independent "nonnegative geometric" numbers of zeros inserted in between. In this paper, that formula will be generalized to the class of weakly stationary, mean zero, complex-valued random sequences, with arbitrary spectral measure.


2018 ◽  
Author(s):  
Pauli Kehayias

Nitrogen-vacancy (NV) defect centers in diamond have generated much interest for their uses in quantum information and sensing. Despite the ongoing improvements in sensitivity and the range of new applications, much about the NV basic physics remains unresolved, which is important to understand in order to fully exploit potential uses. In this work I describe a series of experiments on NV basic properties, applications, and projects in between. First, I describe an NV singlet absorption spectroscopy experiment, which searched for additional NV electronic states and studied the 1A1 phonon modes. Next, I discuss an NV microwave saturation spectroscopy experiment, which is useful for NV thermometry, removes inhomogeneous broadening, and can yield information about diamond magnetic spin bath dynamics. I then describe an NV relaxation experiment that senses GHz-frequency magnetic noise, which we demonstrated using paramagnetic substitutional nitrogen (P1) centers. Finally, I describe open questions on the NV singlet states, saturation spectroscopy, and relaxation (and how to address them), and report on my ongoing work on using NVs for nuclear polarization and rotation sensing.


2016 ◽  
Vol 05 (02) ◽  
pp. 1650006 ◽  
Author(s):  
Marwa Banna ◽  
Florence Merlevède ◽  
Pierre Youssef

In this paper, we obtain a Bernstein-type inequality for the sum of self-adjoint centered and geometrically absolutely regular random matrices with bounded largest eigenvalue. This inequality can be viewed as an extension to the matrix setting of the Bernstein-type inequality obtained by Merlevède et al. [Bernstein inequality and moderate deviations under strong mixing conditions, in High Dimensional Probability V: The Luminy Volume, Institute of Mathematical Statistics Collection, Vol. 5 (Institute of Mathematical Statistics, Beachwood, OH, 2009), pp. 273–292.] in the context of real-valued bounded random variables that are geometrically absolutely regular. The proofs rely on decoupling the Laplace transform of a sum on a Cantor-like set of random matrices.


1984 ◽  
Vol 21 (4) ◽  
pp. 930-934 ◽  
Author(s):  
Donald W. K. Andrews

Certain first-order autoregressive processes are shown not to be strong mixing. A direct proof is given. This proof gives considerably more insight into the nature of the result than do proofs by contradiction. The result and proof help to clarify the relation between the autoregressive and strong mixing conditions.


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