Related papers: A determinantal point process governed by an integ…
As recently proved in generality by Hedenmalm and Wennman, it is a universal behavior of complex random normal matrix models that one finds a complementary error function behavior at the boundary (also called edge) of the droplet as the…
We give a simple algebraic derivation of a useful determinantal identity for multilevel systems such as random matrix chains and finite determinantal point processes, with applications to the calculation of point correlators, gap…
The two-matrix model is defined on pairs of Hermitian matrices $(M_1,M_2)$ of size $n\times n$ by the probability measure $$\frac{1}{Z_n} \exp\left(\textrm{Tr} (-V(M_1)-W(M_2)+\tau M_1M_2)\right)\ dM_1\ dM_2, $$ where $V$ and $W$ are given…
We show the density of eigenvalues for three classes of random matrix ensembles is determinantal. First we derive the density of eigenvalues of product of $k$ independent $n\times n$ matrices with i.i.d. complex Gaussian entries with a few…
Given a positive definite, bounded linear operator $A$ on the Hilbert space $\mathcal{H}_0:=l^2(E)$, we consider a reproducing kernel Hilbert space $\mathcal{H}_+$ with a reproducing kernel $A(x,y)$. Here $E$ is any countable set and…
Akemann, Ipsen and Kieburg recently showed that the squared singular values of products of M rectangular random matrices with independent complex Gaussian entries are distributed according to a determinantal point process with a correlation…
The purpose of this article is to develop a theory behind the occurrence of "path-integral" kernels in the study of extended determinantal point processes and non-intersecting line ensembles. Our first result shows how determinants…
Partially observable Markov decision processes (POMDPs) form a prominent model for uncertainty in sequential decision making. We are interested in constructing algorithms with theoretical guarantees to determine whether the agent has a…
We develop a framework for function classes generated by parametric ridge kernels: one-dimensional kernels composed with affine projections and averaged over a parameter measure. The induced kernels are positive definite, and the resulting…
For applications as varied as Bayesian neural networks, determinantal point processes, elliptical graphical models, and kernel learning for Gaussian processes (GPs), one must compute a log determinant of an $n \times n$ positive definite…
This paper presents a convergence analysis of kernel-based quadrature rules in misspecified settings, focusing on deterministic quadrature in Sobolev spaces. In particular, we deal with misspecified settings where a test integrand is less…
Let $p_n(x)$, $n=0,1,\dots$, be the orthogonal polynomials with respect to a given density $d\mu(x)$. Furthermore, let $d\nu(x)$ be a density which arises from $d\mu(x)$ by multiplication by a rational function in $x$. We prove a formula…
We characterize Fredholm determinants of a class of Hankel composition operators via matrix-valued Riemann-Hilbert problems, for additive and multiplicative compositions. The scalar-valued kernels of the underlying integral operators are…
It is shown that a (curved) projective structure on a smooth manifold determines on the Poisson algebra of smooth, fiberwise-polynomial functions on the cotangent bundle a one-parameter family of graded star products. For a particular value…
The Ginibre point process is given by the eigenvalue distribution of a non-hermitian complex Gaussian matrix in the infinite matrix-size limit. This is a determinantal point process (DPP) on the complex plane ${\mathbb{C}}$ in the sense…
We consider general Markov processes with absorption and provide criteria ensuring the exponential convergence in total variation of the distribution of the process conditioned not to be absorbed. The first one is based on two-sided…
Given any n-tuple of complex numbers, one can canonically define a polynomial of degree n+1 that has the entries of this n-tuple as its critical points. In 2002, Beardon, Carne, and Ng studied a map $\theta\colon \mathbb{C}^n\to…
This paper presents new sufficient conditions for convergence and asymptotic or exponential stability of a stochastic discrete-time system, under which the constructed Lyapunov function always decreases in expectation along the system's…
We find the transition kernels for four Markovian interacting particle systems on the line, by proving that each of these kernels is intertwined with a Karlin-McGregor type kernel. The resulting kernels all inherit the determinantal…
The positive definiteness of real quadratic forms with convolution structures plays an important role in stability analysis for time-stepping schemes for nonlocal operators.In this work, we present a novel analysis tool to handle discrete…