Related papers: The Laguerre process and generalized Hartman--Wats…
We investigate random density matrices obtained by partial tracing larger random pure states. We show that there is a strong connection between these random density matrices and the Wishart ensemble of random matrix theory. We provide…
U-statistics of spatial point processes given by a density with respect to a Poisson process are investigated. In the first half of the paper general relations are derived for the moments of the functionals using kernels from the Wiener-Ito…
The Wang-Landau (WL) algorithm has been widely used for simulations in many areas of physics. Our analysis of the WL algorithm explains its properties and shows that the difference of the largest eigenvalue of the transition matrix in the…
We study discretization effects of the Wilson and staggered Dirac operator with $N_{\rm c}>2$ using chiral random matrix theory (chRMT). We obtain analytical results for the joint probability density of Wilson-chRMT in terms of a…
Suppose that $X=(X_{t})_{t\ge 0}$ is either a general supercritical non-local branching Markov process, or a general supercritical non-local superprocess, on a Luzin space. Here, by ``supercritical" we mean that the mean semigroup of $X$…
We consider the Laguerre Unitary Ensemble (aka, Wishart Ensemble) of sample covariance matrices $A = XX^*$, where $X$ is an $N \times n$ matrix with iid standard complex normal entries. Under the scaling $n = N + \lfloor \sqrt{ 4 c N}…
We discuss contemporaneous aggregation of independent copies of a triangular array of random-coefficient AR(1) processes with i.i.d. innovations belonging to the domain of attraction of an infinitely divisible law W. The limiting aggregated…
In this paper, we establish the law of the iterated logarithm for a wide class of non-stationary, continuous-time Markov processes evolving on Polish spaces. Specifically, our result applies to certain additive functionals of processes…
We study an iterated temporal and contemporaneous aggregation of $N$ independent copies of a strongly stationary subcritical Galton-Watson branching process with regularly varying immigration having index $\alpha \in (0, 2)$. Limits of…
The Laguerre functions $l_{n,\tau}^\alpha$, $n=0,1,\dots$, are constructed from generalized Laguerre polynomials. The functions $l_{n,\tau}^\alpha$ depend on two parameters: scale $\tau>0$ and order of generalization $\alpha>-1$, and form…
In a reinforced Galton-Watson process with reproduction law $\boldsymbol{\nu}$ and memory parameter $q\in(0,1)$, the number of children of a typical individual either, with probability $q$, repeats that of one of its forebears picked…
We consider a particle system in continuous time, discrete population, with spatial motion and nonlocal branching. The offspring's weights and their number may depend on the mother's weight. Our setting captures, for instance, the processes…
We investigate Kesten-Stigum-like results for multi-type Galton-Watson processes with a countable number of types in a general setting, allowing us in particular to consider processes with an infinite total population at each generation.…
Let $\nu=(\nu_1,\ldots,\nu_n)\in (-1,\infty)^n$, $n\ge 1$, and let $\mathcal{L}_\nu$ be a self-adjoint extension of the differential operator \[ L_\nu := \sum_{i=1}^n \left[-\frac{\partial^2}{\partial x_i^2} + x_i^2 +…
A group theoretical formulation of Schramm--Loewner-evolution-type growth processes corresponding to Wess--Zumino--Witten theories is developed that makes it possible to construct stochastic differential equations associated with more…
We study the partial transposition ${W}^\Gamma=(\mathrm{id}\otimes \mathrm{t})W\in M_{dn}(\mathbb C)$ of a Wishart matrix $W\in M_{dn}(\mathbb C)$ of parameters $(dn,dm)$. Our main result is that, with $d\to\infty$, the law of $m{W}^\Gamma$…
This paper is concerned with orthonormal systems in real intervals, given with zero Dirichlet boundary conditions. More specifically, our interest is in systems with a skew-symmetric differentiation matrix (this excludes orthonormal…
We give an approximate formula for the distribution of the largest eigenvalue of real Wishart matrices by the expected Euler characteristic method for the general dimension. The formula is expressed in terms of a definite integral with…
In this paper, we study a certain linear statistics of the unitary Laguerre ensembles, motivated in part by an integrable quantum field theory at finite temperature. It transpires that this is equivalent to the characterization of a…
We study the probability that all eigenvalues of the Laguerre unitary ensemble of n by n matrices are between 0 and t, i.e., the largest eigenvalue distribution. Associated with this probability, in the ladder operator approach for…