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A homogeneous and isotropic cosmological model with a positive cosmological constant is considered. The matter sector is given by a massless scalar field, which can be used as an internal time to deparametrize the theory. The idea is to…
The log Gaussian Cox process is a flexible class of point pattern models for capturing spatial and spatio-temporal dependence for point patterns. Model fitting requires approximation of stochastic integrals which is implemented through…
Computing the distribution of permanents of random matrices has been an outstanding open problem for several decades. In quantum computing, "anti-concentration" of this distribution is an unproven input for the proof of hardness of the task…
Associated to any orthogonal representation of a countable discrete group is an probability measure-preserving action called the Gaussian action. Using the Polish model formalism we developed before, we compute the entropy (in the sense of…
In this paper, we introduce a novel task for machine learning in healthcare, namely personalized modeling of the female hormonal cycle. The motivation for this work is to model the hormonal cycle and predict its phases in time, both for…
We compute the skewness of the matter distribution arising from non-linear evolution and from non-Gaussian initial perturbations. We apply our result to a very generic class of models with non-Gaussian initial conditions and we estimate…
Raw moments are used as a way to estimate species abundance distribution. The almost linear pattern of the log transformation of raw moments across scales allow us to extrapolate species abundance distribution for larger areas. However,…
We consider a linear Hamiltonian system consisting of a classical particle and a scalar field describing by the wave or Klein-Gordon equations with variable coefficients. The initial data of the system are supposed to be a random function…
We study a class of discrete-time random walks in $\mathbb{R}^d$ whose conditional drift decays polynomially in time and grows polynomially with the distance from the origin to the current position. This class is related to several models…
We study moderate deviations of suprema of parametrized sequences of sample bounded Gaussian processes $\{X _x(t), t\in T _x\}$, and first present recent sharp bounds in simple cases. In the almost periodic case, we prove an approximation…
A semi-analytic method is proposed for the generation of realizations of a multivariate process of a given linear correlation structure and marginal distribution. This is an extension of a similar method for univariate processes,…
We study the distribution of the minimum spacing between eigenvalues of a random n by n unitary matrix. The minimum spacing scales as $n^{-4/3}$, not $n^{-2}$ as would be the case for n independent points on the unit circle, illustrating…
Smooth linear statistics of random permutation matrices, sampled under a general Ewens distribution, exhibit an interesting non-universality phenomenon. Though they have bounded variance, their fluctuations are asymptotically non-Gaussian…
Complex systems are often non-stationary, typical indicators are continuously changing statistical properties of time series. In particular, the correlations between different time series fluctuate. Models that describe the multivariate…
Interactions growing slower than a certain exponential of the square of a scalar field, are well behaved when evolved under the functional renormalization group linearised around the Gaussian fixed point. They satisfy properties usually…
This paper develops the theory and methods for modeling a stationary count time series via Gaussian transformations. The techniques use a latent Gaussian process and a distributional transformation to construct stationary series with very…
Vinberg cones and the ambient vector spaces are important in modern statistics of sparse models and of graphical models. The aim of this paper is to study eigenvalue distributions of Gaussian, Wigner and covariance matrices related to…
Computation of moments of transformed random variables is a problem appearing in many engineering applications. The current methods for moment transformation are mostly based on the classical quadrature rules which cannot account for the…
A method to generate new classes of random matrix ensembles is proposed. Random matrices from these ensembles are Lax matrices of classically integrable systems with a certain distribution of momenta and coordinates. The existence of an…
The statistical uncertainty in measuring the primordial density perturbations on a given comoving scale is dictated by the number of independent regions of that scale that are accessible to an observer. This number varies with cosmic time…