Related papers: Asymptotics of Plancherel-type random partitions
We survey a number of models from physics, statistical mechanics, probability theory and combinatorics, which are each described in terms of an orthogonal polynomial ensemble. The most prominent example is apparently the Hermite ensemble,…
In this paper, we analyze the large n-limit for random matrix with external source with three distinct eigenvalues. And we confine ourselves in the Hermite case and the three distinct eigenvalues are $-a,0,a$. For the case $a^2>3$, we…
The aim of this paper is to provide new perspectives on relative finite element accuracy which is usually based on the asymptotic speed of convergence comparison when the mesh size $h$ goes to zero. Starting from a geometrical reading of…
We consider a stochastic individual-based model in continuous time to describe a size-structured population for cell divisions. This model is motivated by the detection of cellular aging in biology. We address here the problem of…
We investigate the product of $n$ complex non-Hermitian, independent random matrices, each of size $N\times N$ in the class of elliptic matrices, with independent identically distributed entries. The joint probability distribution of the…
We use the steepest descents method to study the integral kernel of a family of normal random matrix ensembles with eigenvalue distribution P_{N}(z_{1},...,z_{N}) = Z_{N}^{-1} e^{-N\Sigma_{i=1}^{N}V_{\alpha}(z_{i})}…
This paper introduces a kernel discrepancy-based framework for rerandomization to enhance the precision of causal inference in controlled experiments. We demonstrate that the kernel discrepancy is the key part of the variance upper bound…
We discuss asymptotics for large random planar maps under the assumption that the distribution of the degree of a typical face is in the domain of attraction of a stable distribution with index $\alpha\in(1,2)$. When the number $n$ of…
Distributed machine learning systems have been receiving increasing attentions for their efficiency to process large scale data. Many distributed frameworks have been proposed for different machine learning tasks. In this paper, we study…
We introduce and study the model of simply generated non-crossing partitions, which are, roughly speaking, chosen at random according to a sequence of weights. This framework encompasses the particular case of uniform non-crossing…
The matrix Whittaker kernel has been introduced by A. Borodin in Part IV of the present series of papers. This kernel describes a point process -- a probability measure on a space of countable point configurations. The kernel is expressed…
We consider a Wigner-type ensemble, i.e. large hermitian $N\times N$ random matrices $H=H^*$ with centered independent entries and with a general matrix of variances $S_{xy}=\mathbb E|H_{xy}|^2$. The norm of $H$ is asymptotically given by…
We consider a particle system of the squared Bessel processes with index $\nu > -1$ conditioned never to collide with each other, in which if $-1 < \nu < 0$ the origin is assumed to be reflecting. When the number of particles is finite, we…
We consider a random interval splitting process, in which the splitting rule depends on the empirical distribution of interval lengths. We show that this empirical distribution converges to a limit almost surely as the number of intervals…
The randomized quantum marginal problem asks about the joint distribution of the partial traces ("marginals") of a uniform random Hermitian operator with fixed spectrum acting on a space of tensors. We introduce a new approach to this…
Motivated by a question of V. Bergelson and F. K. Richter (2017), we obtain asymptotic formulas for the number of relatively prime tuples composed of positive integers $n\le N$ and integer parts of polynomials evaluated at $n$. The error…
We consider a nonparametric regression setup, where the covariate is a random element in a complete separable metric space, and the parameter of interest associated with the conditional distribution of the response lies in a separable…
This paper introduces a multilevel kernel-based approximation method to estimate efficiently solutions to elliptic partial differential equations (PDEs) with periodic random coefficients. Building upon the work of Kaarnioja, Kazashi, Kuo,…
Two closely related discrete probability distributions are introduced. In each case the support is a set of vectors in $\mathbb{R}^n$ obtained from the partitions of the fixed positive integer $n$. These distributions arise naturally when…
In these lecture notes we present some connections between random matrices, the asymmetric exclusion process, random tilings. These three apparently unrelated objects have (sometimes) a similar mathematical structure, an interlacing…