arXiv subjects

David Barrera

Publications and source records attributed to David Barrera.

25 records · Page 2Linked to original sources

arXiv2016

Quenched Asymptotics for the Discrete Fourier Transforms of a Stationary Process

In this dissertation, we show that the Central Limit Theorem and the Invariance Principle for Discrete Fourier Transforms discovered by Peligrad and Wu can be extended to the quenched setting. We show that the random normalization introduced to extend these results is necessary and we discuss its meaning. We also show the validity of the quenched Invariance Principle for fixed frequencies under some conditions of weak dependence. In particular, we show that this result holds in the martingale case. The discussion needed for the proofs allows us to show some general facts apparently not noticed before in the theory of convergence in distribution. In particular, we show that in the case of separable metric spaces the set of test functions in the Portmanteau theorem can be reduced to a countable one, which implies that the notion of quenched convergence, given in terms of convergence a.s. of conditional expectations, specializes in the right way in the regular case when the state space is metrizable and second-countable. We also collect and organize several disperse facts from the existing theory in a consistent manner towards the statistical spectral analysis of the Discrete Fourier Transforms, providing a comprehensive introduction to topics in this theory that apparently have not been systematically addressed in a self-contained way by previous references.

math.PR↗

arXiv2016

HORNET: High-speed Onion Routing at the Network Layer

We present HORNET, a system that enables high-speed end-to-end anonymous channels by leveraging next generation network architectures. HORNET is designed as a low-latency onion routing system that operates at the network layer thus enabling a wide range of applications. Our system uses only symmetric cryptography for data forwarding yet requires no per-flow state on intermediate nodes. This design enables HORNET nodes to process anonymous traffic at over 93 Gb/s. HORNET can also scale as required, adding minimal processing overhead per additional anonymous channel. We discuss design and implementation details, as well as a performance and security evaluation.

cs.CR↗

arXiv2016

On the functional CLT for stationary Markov Chains started at a point

We present a general functional central limit theorem started at a point also known under the name of quenched. As a consequence, we point out several new classes of stationary processes, defined via projection conditions, which satisfy this type of asymptotic result. One of the theorems shows that if a Markov chain is stationary ergodic and reversible, this result holds for bounded additive functionals of the chain which have a martingale coboundary in L_1 representation. Our results are also well adapted for strongly mixing sequences providing for this case an alternative, shorter approach to some recent results in the literature.

math.PR↗

arXiv2016

Quenched limit theorems for Fourier transforms and periodogram

In this paper, we study the quenched central limit theorem for the discrete Fourier transform. We show that the Fourier transform of a stationary ergodic process, suitable centered and normalized, satisfies the quenched CLT conditioned by the past sigma algebra. For functions of Markov chains with stationary transitions, this means that the CLT holds with respect to the law of the chain started at a point for almost all starting points. It is necessary to emphasize that no assumption of irreducibility with respect to a measure or other regularity conditions are imposed for this result. We also discuss necessary and sufficient conditions for the validity of quenched CLT without centering. The results are highly relevant for the study of the periodogram of a Markov process with stationary transitions which does not start from equilibrium. The proofs are based of a nice blend of harmonic analysis, theory of stationary processes, martingale approximation and ergodic theory.

math.PR↗

arXiv2015

Bootstrapping Real-world Deployment of Future Internet Architectures

The past decade has seen many proposals for future Internet architectures. Most of these proposals require substantial changes to the current networking infrastructure and end-user devices, resulting in a failure to move from theory to real-world deployment. This paper describes one possible strategy for bootstrapping the initial deployment of future Internet architectures by focusing on providing high availability as an incentive for early adopters. Through large-scale simulation and real-world implementation, we show that with only a small number of adopting ISPs, customers can obtain high availability guarantees. We discuss design, implementation, and evaluation of an availability device that allows customers to bridge into the future Internet architecture without modifications to their existing infrastructure.

cs.NI↗

arXiv2015

SCION Five Years Later: Revisiting Scalability, Control, and Isolation on Next-Generation Networks

The SCION (Scalability, Control, and Isolation on Next-generation Networks) inter-domain network architecture was proposed to address the availability, scalability, and security shortcomings of the current Internet. This paper presents a retrospective of the SCION goals and design decisions, its attacker model and limitations, and research highlights of work conducted in the 5 years following SCION's initial publication.

cs.NI↗

arXiv2014

An Example of non-quenched Convergence in the Conditional CLT for Discrete Fourier Transforms

A recent result by Barrera and Peligrad shows that the quenched Central Limit Theorem holds for the discrete Fourier transforms (DFT) of a stationary process in $L^2$ if a "random" centering is used. In this note we show that this is a necessary condition by providing an example of a process satisfying the hypothesis of such theorem for which the DFT, without random centering, do not satisfy a quenched limit theorem. The DFT of this process, by previous results by Peligrad and Wu, satisfy the corresponding CLT in the annealed sense.

math.PR↗