Related papers: Integrability conditions for the Grushin and Marti…

In this paper we discuss general tridiagonal matrix models which are natural extensions of the ones given by Dumitriu and Edelman. We prove here the convergence of the distribution of the eigenvalues and compute the limiting distributions…

Because of its mathematical tractability, the Gaussian mixture model holds a special place in the literature for clustering and classification. For all its benefits, however, the Gaussian mixture model poses problems when the data is skewed…

The Ginibre ensemble of complex random matrices is studied. The complex valued random variable of second difference of complex energy levels is defined. For the N=3 dimensional ensemble are calculated distributions of second difference, of…

In a previous study, we formulated a framework of the entropy-based equilibrium statistical mechanics for self-gravitating systems. This theory is based on the Boltzmann-Gibbs entropy and includes the generalized virial equations as…

We transfer the scheme of constructing differential reductions, developed recently for the case of the Manakov-Santini hierarchy, to the general multidimensional case. We consider in more detail the four-dimensional case, connected with the…

In this article we show the existence of limiting spectral distribution of a symmetric random matrix whose entries come from a stationary Gaussian process with covariances satisfying a summability condition. We provide an explicit…

Consider the ensemble of real symmetric Toeplitz matrices, each independent entry an i.i.d. random variable chosen from a fixed probability distribution p of mean 0, variance 1, and finite higher moments. Previous investigations showed that…

We study distributionally robust optimization with Sinkhorn distance -- a variant of Wasserstein distance based on entropic regularization. We derive a convex programming dual reformulation for general nominal distributions, transport…

Let $G=-\Delta-|x|^2\partial_{t}^2$ denote the Grushin operator on $\mathbb{R}^{n+1}$. The aim of this paper is two fold. In the first part, due to the non-dispersive phenomena of the Grushin-Schr\"odinger equation on $\mathbb{R}^{n+1}$, we…

Consider the ensemble of Real Symmetric Toeplitz Matrices, each entry iidrv from a fixed probability distribution p of mean 0, variance 1, and finite higher moments. The limiting spectral measure (the density of normalized eigenvalues)…

We consider interior penalty discontinuous Galerkin discretizations of time-harmonic wave propagation problems modeled by the Helmholtz equation, and derive novel a priori and a posteriori estimates. Our analysis classically relies on…

Local minima also known as inherent structures are expected to play an essential role for the behavior of spin glasses. Here, we propose techniques to efficiently sample these configurations in Monte Carlo simulations. For the…

We consider Gaussian distributions on certain Riemannian symmetric spaces. In contrast to the Euclidean case, it is challenging to compute the normalization factors of such distributions, which we refer to as partition functions. In some…

We introduce an extension of finite mixture models by incorporating skew-normal distributions within a Hidden Markov Model framework. By assuming a constant transition probability matrix and allowing emission distributions to vary according…

We give two new simple characterizations of the Cauchy distribution by using the M\"obius and Mellin transforms. They also yield characterizations of the circular Cauchy distribution and the mixture Cauchy model.

This paper proves joint convergence of the approximation error for several stochastic integrals with respect to local Brownian semimartingales, for nonequidistant and random grids. The conditions needed for convergence are that the Lebesgue…

For a pair of coupled rectangular random matrices we consider the squared singular values of their product, which form a determinantal point process. We show that the limiting mean distribution of these squared singular values is described…

Doubly intractable distributions arise in many settings, for example in Markov models for point processes and exponential random graph models for networks. Bayesian inference for these models is challenging because they involve intractable…

Using generating function methods for diagonalizing the transition matrix in 2-Urn models, we provide a complete classification into solvable and unsolvable subclasses, with further division of the solvable models into the Martingale and…

Bayesian methods constitute a popular approach for estimating the conditional independence structure in Gaussian graphical models, since they can quantify the uncertainty through the posterior distribution. Inference in this framework is…