相关论文: Random partitions and the Gamma kernel

The usual formulas for the correlation functions in orthogonal and symplectic matrix models express them as quaternion determinants. From this representation one can deduce formulas for spacing probabilities in terms of Fredholm…

We establish the asymptotic theory in quantile autoregression when the model parameter is specified with respect to moderate deviations from the unit boundary of the form (1 + c / k) with a convergence sequence that diverges at a rate…

Empirical observation of high dimensional phenomena, such as the double descent behaviour, has attracted a lot of interest in understanding classical techniques such as kernel methods, and their implications to explain generalization…

We study the asymptotic behaviour of random integer partitions under a new probability law that we introduce, the Plancherel-Hurwitz measure. This distribution, which has a natural definition in terms of Young tableaux, is a deformation of…

We present Random Partition Kernels, a new class of kernels derived by demonstrating a natural connection between random partitions of objects and kernels between those objects. We show how the construction can be used to create kernels…

We consider the nonparametric estimation of the univariate heavy tailed probability density function (pdf) with a support on $[0,\infty)$ by independent data. To this end we construct the new kernel estimator as a combination of the…

We develop the study of a particular class of biorthogonal measures, encompassing at the same time several random matrix models and partition functions of polymers. This general framework allows us to characterize the partition functions of…

We consider a two-dimensional diffusion process in a two-layered plane, governed by distinct covariance matrices in the upper and lower half-planes and by two drift vectors pointed away from the $x$-axis. We first analyze the case where the…

In this paper, by mapping datasets to a set of non-linear coherent states, the process of encoding inputs in quantum states as a non-linear feature map is re-interpreted. As a result of this fact that the Radial Basis Function is recovered…

In this paper, we proceed to study the nonlocal diffusion problem proposed by Li and Wang [8], where the left boundary is fixed, while the right boundary is a nonlocal free boundary. We first give some accurate estimates on the longtime…

Conditional copula models allow dependence structures to vary with observed covariates while preserving a separation between marginal behavior and association. We study the uniform asymptotic behavior of kernel-weighted local likelihood…

Ratio of medians or other suitable quantiles of two distributions is widely used in medical research to compare treatment and control groups or in economics to compare various economic variables when repeated cross-sectional data are…

An importance sampling method based on Generalized Feynman-Kac method has been used to calculate the mean values of quantum observables from quantum correlation functions for many body systems both at zero and finite temperature.…

For a finite random graph, we defined a simple model of statistical mechanics. We obtain an annealed asymptotic result for the random partition function for this model on finite random graphs as n; the size of the graph is very large. To…

The discrete kernel method was developed to estimate count data distributions, distinguishing discrete associated kernels based on their asymptotic behaviour. This study investigates the class of discrete asymmetric kernels and their…

In this study we consider the $\Gamma$-limit of a highly oscillatory Riemannian metric length functional as its period tends to 0. The metric coefficient takes values in either $\{1,\infty\}$ or $\{1,\beta \varepsilon^{-p}\}$ where…

One of the most important questions in quantum information theory is the so-called separability problem. It involves characterizing the set of separable (or, equivalently entangled) states among mixed states of a multipartite quantum…

The characterization of quantum correlations, being stronger than classical, yet weaker than those appearing in non-signaling models, still poses many riddles. In this work we show that the extent of binary correlations in a general class…

We study the outliers for two models which have an interesting connection. On the one hand, we study a specific class of planar Coulomb gases which are determinantal. It corresponds to the case where the confining potential is the…

An essential feature of genuine quantum correlation is the simultaneous existence of correlation in complementary bases. We reveal this feature of quantum correlation by defining measures based on invariance under a basis change. For a…