Related papers: Exponential-Uniform Identities Related to Records
A random phenomenon may have two sources of random variation: an unstable identity and a set of external variation-generating factors. When only a single source is active, two mutually exclusive extreme scenarios may ensue that result in…
Motivated by some binomial coefficients identities encountered in our approach to the enumeration of convex polyominoes, we prove some more general identities of the same type, one of which turns out to be related to a strange evaluation of…
Determinantal point processes are models for regular spatial point patterns, with appealing probabilistic properties. We present their spatio-temporal counterparts and give examples of these models, based on spatio-temporal covariance…
Random matrix ensembles are introduced that respect the local tensor structure of Hamiltonians describing a chain of $n$ distinguishable spin-half particles with nearest-neighbour interactions. We prove a central limit theorem for the…
Boundary-induced pattern formation from a spatially uniform state is investigated using one-dimensional reaction-diffusion equations. The temporal oscillation is successively transformed into a spatially periodic pattern, triggered by…
Interesting properties of the partitions of a finite field $\mathbb F_q$ induced by the combination of involutions and trace maps are studied. The special features of involutions of the form $\frac{u}{z}$, $u$ being a fixed element of…
A very elementary model of a single positive hermitian random matrix coupled to an external matrix is defined and studied. Expanding the exact effective action around its classical solution leads to the ``quantum Penner action'', from which…
We exhibit explicit expressions, in terms of components, of discriminants, determinants, characteristic polynomials and polynomial identities for matrices of higher rank. We define permutation tensors and in term of them we construct…
A new characterization of the exponential distribution is obtained. It is based on an equation involving randomly shifted (translated) order statistics. No specific distribution is assumed for the shift random variables. The proof uses a…
We consider Poissonian pair correlations (PPC) for uniformly distributed sequences of random numbers with a dependency structure. More specifically, we treat two classes of dependent random variables which have widely been studied in the…
Exponential families comprise a broad class of statistical models and parametric families like normal distributions, binomial distributions, gamma distributions or exponential distributions. Thereby the formal representation of its…
Causal inference quantifies cause-effect relationships by estimating counterfactual parameters from data. This entails using \emph{identification theory} to establish a link between counterfactual parameters of interest and distributions…
We establish a number of "concatenation theorems" that assert, roughly speaking, that if a function exhibits "polynomial" (or "Gowers anti-uniform", "uniformly almost periodic", or "nilsequence") behaviour in two different directions…
We consider the characteristic polynomials of random unitary matrices $U$ drawn from various circular ensembles. In particular, the statistics of the coefficients of these polynomials are studied. The variances of these ``secular…
In this paper, we study exponential random graph models subject to certain constraints. We obtain some general results about the asymptotic structure of the model. We show that there exists non-trivial regions in the phase plane where the…
We consider the Rosenzweig-Porter model of random matrix which interpolates between Poisson and gaussian unitary statistics and compute exactly the two-point correlation function. Asymptotic formulas for this function are given near the…
We study a class of Hermitian random matrices which includes and generalizes Wigner matrices, heavy-tailed random matrices, and sparse random matrices such as the adjacency matrices of Erdos-Renyi random graphs with p ~ 1/N. Our NxN random…
A central question in random matrix theory is universality. When an emergent phenomena is observed from a large collection of chosen random variables it is natural to ask if this behavior is specific to the chosen random variable or if the…
The convergence of a sequence of point processes with dependent points, defined by a symmetric function of iid high-dimensional random vectors, to a Poisson random measure is proved. This also implies the convergence of the joint…
We study stochastic billiards in infinite planar domains with curvilinear boundaries: that is, piecewise deterministic motion with randomness introduced via random reflections at the domain boundary. Physical motivation for the process…