Related papers: The intertwining property for Laguerre processes w…
In Random Matrix Theory the local correlations of the Laguerre and Jacobi Unitary Ensemble in the hard edge scaling limit can be described in terms of the Bessel kernel (containing a parameter $\alpha$). In particular, the so-called hard…
We place ourselves in the setting of high-dimensional statistical inference where the number of variables $p$ in a dataset of interest is of the same order of magnitude as the number of observations $n$. We consider the spectrum of certain…
In this note we consider a family of nonlinear (conditional) expectations that can be understood as a multidimensional diffusion with uncertain drift and certain volatility. Here, the drift is prescribed by a set-valued function that…
Data sites selected from modeling high-dimensional problems often appear scattered in non-paternalistic ways. Except for sporadic clustering at some spots, they become relatively far apart as the dimension of the ambient space grows. These…
We give a substitute to Feller property for semigroups of time-changed processes; under some conditions this leads to establish sufficient (new) conditions for the semigroups to be Feller. Moreover, given a standard process and a sequence…
We measure electrical transport on networks of single wall nanotube of different origin as a function of temperature T, voltage V and pressure P . We observe Luttinger liquid (LL) behavior, a conductance T^alpha and a dynamic conductance…
We consider a family of determinantal random point processes on the two-dimensional lattice and prove that members of our family can be interpreted as a kind of Gibbs ensembles of nonintersecting paths. Examples include probability measures…
The main result of this paper, Theorem 1.5, establishes a conjecture of Lyons and Peres: for a determinantal point process governed by a reproducing kernel, the system of kernels sampled at the particles of a random configuration is…
In this paper we derive an efficient algorithm to learn the parameters of structured predictors in general graphical models. This algorithm blends the learning and inference tasks, which results in a significant speedup over traditional…
We extend inner fluctuations to spectral triples that do not fulfill the first-order condition. This involves the addition of a quadratic term to the usual linear terms. We find a semi-group of inner fluctuations, which only depends on the…
It is long known that the rational Calogero model describing n identical particles on a line with inverse-square mutual interaction potential is quantum superintegrable. We review the (nonlinear) algebra of the conserved quantum charges and…
We define Laguerre and Jacobi analogues of the Warren process. That is, we construct local dynamics on a triangular array of particles so that the projections to each level recover the Laguerre and Jacobi eigenvalue processes of…
A recently developed wavelet based approach is employed to characterize the scaling behavior of spectral fluctuations of random matrix ensembles, as well as complex atomic systems. Our study clearly reveals anti-persistent behavior and…
This work proposed kernel selection approaches for probabilistic classifiers based on features produced by the convolutional encoder of a variational autoencoder. Particularly, the developed methodologies allow the selection of the most…
We present a novel attention-based model for discrete event data to capture complex non-linear temporal dependence structures. We borrow the idea from the attention mechanism and incorporate it into the point processes' conditional…
Intertwining relations for $N$-particle Calogero-like models with internal degrees of freedom are investigated. Starting from the well known Dunkl-Polychronakos operators, we construct new kind of local (without exchange operation)…
In this paper we consider the kernel of the radially deformed Fourier transform introduced in the context of Clifford analysis in [10]. By adapting the Laplace transform method from [4], we obtain the Laplace domain expressions of the…
A model of interacting one--dimensional fermions confined to a harmonic trap is proposed. The model is treated analytically to all orders of the coupling constant by a method analogous to that used for the Luttinger model. As a first…
The purpose of this paper is to investigate the distribution of zeros of entire functions which can be represented as the Fourier transforms of certain admissible kernels. The principal results bring to light the intimate connection between…
We investigate the capabilities of neural inverse procedural modeling to infer high-quality procedural yarn models with fiber-level details from single images of depicted yarn samples. While directly inferring all parameters of the…