Related papers: The multiplicative constant for the Meijer-$G$ ker…
The Laplace transform of partial sums of the square of a non-centered Gauss-Markov process, conditioning on its starting point, is explicitly computed. The parameters of multiplicative ergodicity are deduced.
We derive exact analytical expressions for correlation functions of singular values of the product of $M$ Ginibre matrices of size $N$ in the double scaling limit $M,N\rightarrow \infty$. The singular value statistics is described by a…
In this paper we prove a randomized difference norm characterization for Bessel potential spaces with values in UMD Banach spaces. The main ingredients are $\mathcal{R}$-boundedness results for Fourier multiplier operators, which are of…
The paper considers the problem of estimating a $p\geq2$\ dimensional mean vector of a multivariate conditionally normal distribution under quadratic loss. The problem of this type arises when estimating the parameters in a continuous time…
The Gamma kernel is a projection kernel of the form (A(x)B(y)-B(x)A(y))/(x-y), where A and B are certain functions on the one-dimensional lattice expressed through Euler's Gamma function. The Gamma kernel depends on two continuous…
We study the multiplicative statistics associated to the limiting determinantal point process describing unitary random matrices with a critical edge point, where limiting density vanishes like a power 5/2. We prove that these statistics…
Determinantal point processes are point processes whose correlation functions are given by determinants of matrices. The entries of these matrices are given by one fixed function of two variables, which is called the kernel of the point…
We present a solution to a problem suggested by Philippe Biane: We prove that a certain Plancherel-type probability distribution on partitions converges, as partitions get large, to a new determinantal random point process on the set…
We develop sampling formulas for high-dimensional functions in reproducing kernel Hilbert spaces, where we rely on irregular samples that are taken at determining sequences of data points. We place particular emphasis on sampling formulas…
In this paper, we construct the Bessel line ensemble, a countable collection of continuous random curves. This line ensemble is stationary under horizontal shifts with the Bessel point process as its one-time marginal. Its finite…
The Bures metric is a natural choice in measuring the distance of density operators representing states in quantum mechanics. In the past few years a random matrix ensemble and the corresponding joint probability density function of its…
A generalized linear point process is specified in terms of an intensity that depends upon a linear predictor process through a fixed non-linear function. We present a framework where the linear predictor is parametrized by a Banach space…
We study the total mass of high points in a random model for the Riemann-Zeta function. We consider the same model as in [8], [2], and build on the convergence to 'Gaussian' multiplicative chaos proved in [14]. We show that the total mass…
In order to compute the log-likelihood for high dimensional spatial Gaussian models, it is necessary to compute the determinant of the large, sparse, symmetric positive definite precision matrix, Q. Traditional methods for evaluating the…
The unitary group with the Haar probability measure is called Circular Unitary Ensemble. All the eigenvalues lie on the unit circle in the complex plane and they can be regarded as a determinantal point process on $\mathbb{S}^1$. It is also…
The product of M complex random Gaussian matrices of size N has recently been studied by Akemann, Kieburg and Wei. They showed that, for fixed M and N, the joint probability distribution for the squared singular values of the product matrix…
We study the role of multiplicative stochastic processes in the description of the dynamics of an order parameter near a critical point. We study equilibrium, as well as, out-of-equilibrium properties. By means of a functional formalism, we…
We work out a generalization of the Szeg\"o limit theorems on the determinant of large matrices. We focus on matrices with nonzero leading principal minors and elements that decay to zero exponentially fast with the distance from the main…
The singular values squared of the random matrix product $Y = G_r G_{r-1} \cdots G_1 (G_0 + A)$, where each $G_j$ is a rectangular standard complex Gaussian matrix while $A$ is non-random, are shown to be a determinantal point process with…
The results of this paper are 3-folded. Firstly, for any stationary determinantal process on the integer lattice, induced by strictly positive and strictly contractive involution kernel, we obtain the necessary and sufficient condition for…