Related papers: A new structure for analyzing discrete scale invar…
We adapt the classical definition of locally stationary processes in discrete-time to the continuous-time setting and obtain equivalent representations in the time and frequency domain. From this, a unique time-varying spectral density is…
Layered stable (multivariate) distributions and processes are defined and studied. A layered stable process combines stable trends of two different indices, one of them possibly Gaussian. More precisely, in short time, it is close to a…
We present a scalable method for the tomography of large multiqubit quantum registers. It acquires information about the permutationally invariant part of the density operator, which is a good approximation to the true state in many,…
We propose a scalable framework for inference in an inhomogeneous Poisson process modeled by a continuous sigmoidal Cox process that assumes the corresponding intensity function is given by a Gaussian process (GP) prior transformed with a…
Novel results for the self-consistent single-particle spectral function and self-energy are presented for non-degenerate one-component Coulomb systems at various densities and temperatures. The GW^0-method for the dynamical self-energy is…
Due to the mechanism of recording, the presence of multiple transactions at each recording time becomes a common feature for high-frequency data in financial market. Using random matrix theory, this paper considers the estimation of…
Transverse deflecting structures (TDS) are widely used in accelerator physics to measure the longitudinal density of particle bunches. When used in combination with a dispersive section, the whole longitudinal phase space density can be…
Based on theoretical argument and experimental evidence, we conjecture that structure functions of turbulent times series exhibit log-periodic modulations decorating their power law dependence. In order to provide ironclad experimental…
Temporal point processes offer a powerful framework for sampling from discrete distributions, yet they remain underutilized in existing literature. We show how to construct, for any target multivariate count distribution with…
We compute the spectral statistics of the sum H of two independent complex Wishart matrices, each of which is correlated with a different covariance matrix. Random matrix theory enjoys many applications including sums and products of random…
The estimation of the covariance function of a stochastic process, or signal, is of integral importance for a multitude of signal processing applications. In this work, we derive closed-form expressions for the variance of covariance…
This paper studies the case of possibly high-dimensional covariates in the regression discontinuity design (RDD) analysis. In particular, we propose estimation and inference methods for the RDD models with covariate selection which perform…
Applying the replica method of statistical mechanics, we evaluate the eigenvalue density of the large random matrix (sample covariance matrix) of the form $J = A^{\rm T} A$, where $A$ is an $M \times N$ real sparse random matrix. The…
Spectral density functions quantify how environmental modes couple to quantum systems and govern their open dynamics. Inferring such frequency-dependent functions from time-domain measurements is an ill-conditioned inverse problem. Here, we…
In this paper we explore a covariance spectral modelling strategy for spatial-temporal processes which involves a spectral approach for time but a covariance approach for space.It facilitates the analysis of coherence between the temporal…
The study of multidimensional stochastic processes involves complex computations in intricate functional spaces. In particular, the diffusion processes, which include the practically important Gauss-Markov processes, are ordinarily defined…
We develop two new classes of space-time Gaussian process models by specifying covariance functions using what we call a half-spectral representation. The half-spectral representation of a covariance function, $K$, is a special case of…
Discrete stability extends the classical notion of stability to random elements in discrete spaces by defining a scaling operation in a randomised way: an integer is transformed into the corresponding binomial distribution. Similarly…
Let X^{(k)}(t) = (X_1(t), ..., X_k(t)) denote a k-vector of i.i.d. random variables, each taking the values 1 or 0 with respective probabilities p and 1-p. As a process indexed by non-negative t, $X^{(k)}(t)$ is constructed--following…
In this work, we study general Dirichlet coalescents, which are a family of Xi-coalecents constructed from i.i.d mass partitions, and are an extension of the symmetric coalescent. This class of models is motivated by population models with…