Amplitude And Phase Variation Of Point Processes

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Certification of the efficient random number generation technique based on single-photon detector arrays and time-to-digital converters

Edoardo Charbon, Samuel Burri

True random number generators (TRNGs) allow the generation of true random bit sequences, guaranteeing the unpredictability and perfect balancing of the generated values. TRNGs can be realised from the sampling of quantum phenomena, for instance, the detect ...

Wiley2021

Sparsely Observed Functional Time Series: Theory and Applications

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Functional time series is a temporally ordered sequence of not necessarily independent random curves. While the statistical analysis of such data has been traditionally carried out under the assumption of completely observed functional data, it may well ha ...

EPFL2021

Statistical limits of high-dimensional inference problems

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This thesis focuses on two kinds of statistical inference problems in signal processing and data science. The first problem is the estimation of a structured informative tensor from the observation of a noisy tensor in which it is buried. The structure com ...

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Functional registration and local variations: Identifiability, rank, and tuning

Victor Panaretos, Anirvan Chakraborty

We develop theory and methodology for the problem of nonparametric registration of functional data that have been subjected to random deformation (warping) of their time scale. The separation of this phase variation ("horizontal" variation) from the amplit ...

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Normal approximation of the solution to the stochastic heat equation with Levy noise

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Given a sequence L & x2d9;epsilon of Levy noises, we derive necessary and sufficient conditions in terms of their variances sigma 2(epsilon) such that the solution to the stochastic heat equation with noise sigma(epsilon)-1L & x2d9;epsilon converges in law ...

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Max-infinitely divisible models and inference for spatial extremes

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For many environmental processes, recent studies have shown that the dependence strength is decreasing when quantile levels increase. This implies that the popular max-stable models are inadequate to capture the rate of joint tail decay, and to estimate jo ...

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Gaussian and sparse processes are limits of generalized Poisson processes

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The theory of sparse stochastic processes offers a broad class of statistical models to study signals, far beyond the more classical class of Gaussian processes. In this framework, signals are represented as realizations of random processes that are soluti ...

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An Operational Approach to Information Leakage

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Given two random variables X and Y , an operational approach is undertaken to quantify the "leakage" of information from X to Y . The resulting measure L (X -> Y) is called maximal leakage, and is defined as the multiplicative increase, upon observing Y , ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

The probability of intransitivity in dice and close elections

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We study the phenomenon of intransitivity in models of dice and voting. First, we follow a recent thread of research for n-sided dice with pairwise ordering induced by the probability, relative to 1/2, that a throw from one die is higher than the other. We ...

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Strong convergence of multivariate maxima

Simone Padoan, Stefano Rizzelli

It is well known and readily seen that the maximum of n independent and uniformly on [0, 1] distributed random variables, suitably standardised, converges in total variation distance, as n increases, to the standard negative exponential distribution. We ex ...

CAMBRIDGE UNIV PRESS2020

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Certification of the efficient random number generation technique based on single-photon detector arrays and time-to-digital converters

Edoardo Charbon, Samuel Burri

Wiley2021