Related papers: Conditional measures of generalized Ginibre point …
We propose a nonparametric method for estimating the conditional quantile function that admits a generalized additive specification with an unknown link function. This model nests single-index, additive, and multiplicative quantile…
The asymptotic behaviour of empirical measures has been studied extensively. In this paper, we consider empirical measures of given subordinated processes on complete (not necessarily compact) and connected Riemannian manifolds with…
It is proved that to every invariant measure of a compact dynamical system one can associate a certain asymptotic pseudo orbit such that any point asymptotically tracing in average that pseudo orbit is generic for the measure. It follows…
We present an operator-free, measure-theoretic approach to the conditional mean embedding (CME) as a random variable taking values in a reproducing kernel Hilbert space. While the kernel mean embedding of unconditional distributions has…
We demonstrate that a system of bi-orthogonal polynomials and their associated functions corresponding to a regular semi-classical weight on the unit circle constitute a class of general classical solutions to the Garnier systems by…
We establish large deviation principles for the extremal eigenvalues of the Ginibre ensembles with good rate functions. In contrast to the typical estimates for the extremal eigenvalues, the large deviations for the real Ginibre ensemble…
We formulate and prove a very general relative version of the Dobrushin-Lanford-Ruelle theorem which gives conditions on constraints of configuration spaces over a finite alphabet such that for every absolutely summable relative…
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…
A new notion of typicality for arbitrary probability measures on standard Borel spaces is proposed, which encompasses the classical notions of weak and strong typicality as special cases. Useful lemmas about strong typical sets, including…
In this paper, we study a class of multilinear Gibbs measures with Hamiltonian given by a generalized $\mathrm{U}$-statistic and with a general base measure. Expressing the asymptotic free energy as an optimization problem over a space of…
Recently, the joint probability density functions of complex eigenvalues for products of independent complex Ginibre matrices have been explicitly derived as determinantal point processes. We express truncated series coming from the…
In the article we discuss the notion of the generalized invariant manifold introduced in our previous study. In the literature the method of the differential constraints is well known as a tool for constructing particular solutions for the…
We generalize the measurement using an expanded concept of cover, in order to provide a new approach to size of set other than cardinality. The generalized measurement has application backgrounds such as a generalized problem in dimension…
An elementary derivation of the Borodin-Sinclair-Forrester-Nagao Pfaffian point process, which characterises the law of real eigenvalues for the real Ginibre ensemble in the large matrix size limit, uses the averages of products of…
We derive an explicit simple formula for expectations of all Schur functions in the real Ginibre ensemble. It is a positive integer for all entries of the partition even and zero otherwise. The result can be used to determine the average of…
We study linear statistics of a class of determinantal processes which interpolate between Poisson and GUE/Ginibre statistics in dimension 1 or 2. These processes are obtained by performing an independent Bernoulli percolation on the…
Ensembles of complex symmetric, and complex self dual random matrices are known to exhibit local statistical properties distinct from those of the non-Hermitian Ginibre ensembles. On the other hand, in distinction to the latter, the joint…
For a broad class of point processes, including determinantal point processes, we construct associated marked and conditional ensembles, which allow to study a random configuration in the point process, based on information about a randomly…
We introduce a general framework to deterministically construct binary measurement matrices for compressed sensing. The proposed matrices are composed of (circulant) permutation submatrix blocks and zero submatrix blocks, thus making their…
The Papangelou intensities of determinantal (or fermion) point processes are investigated. These exhibit a monotonicity property expressing the repulsive nature of the interaction, and satisfy a bound implying stochastic domination by a…