Related papers: Bicovariograms and Euler characteristic I. Regular…
This paper develops methods to study the distribution of Eulerian statistics defined by second-order recurrence relations. We define a random process to decompose the statistics over compositions of integers. It is shown that the numbers of…
We consider a static linear panel model with both correlated and uncorrelated random coefficients, where the former can depend arbitrarily on observable regressors while the latter are independent of them. We provide sufficient conditions…
The properties of the normal distribution under linear transformation, as well the easy way to compute the covariance matrix of marginals and conditionals, offer a unique opportunity to get an insight about several aspects of uncertainties…
We establish the first quantitative Berry-Esseen bounds for edge eigenvector statistics in random regular graphs. For any $d$-regular graph on $N$ vertices with fixed $d \geq 3$ and deterministic unit vector $\mathbf{q} \perp \mathbf{e}$,…
A set of four scalar conditions involving normal components of the fields D and B and their normal derivatives at a planar surface is introduced, among which different pairs can be chosen to represent possible boundary conditions for the…
Nonnegative measures that are solutions to a transport equation with continuous coefficients have been widely studied. Because of the low regularity of the associated vector field, there is no natural flow since nonuniqueness of integral…
A pair of sequences of natural numbers is called planar if there exists a simple, bipartite, planar graph for which the given sequences are the degree sequences of its parts. For a pair to be planar, the sums of the sequences have to be…
Concerning bivariate least squares linear regression, the classical results obtained for extreme structural models in earlier attempts are reviewed using a new formalism in terms of deviation (matrix) traces which, for homoscedastic data,…
I propose an estimation algorithm for Exponential Random Graph Models (ERGM), a popular statistical network model for estimating the structural parameters of strategic network formation in economics and finance. Existing methods often…
We consider linear structural equation models that are associated with mixed graphs. The structural equations in these models only involve observed variables, but their idiosyncratic error terms are allowed to be correlated and…
In this paper we briefly review the main methodological aspects concerned with the application of the Bayesian approach to model choice and model averaging in the context of variable selection in regression models. This includes prior…
A variety of descent and major-index statistics have been defined for symmetric groups, hyperoctahedral groups, and their generalizations. Typically associated to pairs of such statistics is an Euler--Mahonian distribution, a bivariate…
In this paper we extend the notion of the Euler characteristic to persistent homology and give the relationship between the Euler integral of a function and the Euler characteristic of the function's persistent homology. We then proceed to…
Exponential random graph models (ERGMs) are a widely used framework for network data, enabling hypothesis testing on the structural mechanisms underlying observed networks. Bayesian ERGMs provide principled uncertainty quantification and…
Random walks on regular bounded degree expander graphs have numerous applications. A key property of these walks is that they converge rapidly to the uniform distribution on the vertices. The recent study of expansion of high dimensional…
The random connection model is a random graph whose vertices are given by the points of a Poisson process and whose edges are obtained by randomly connecting pairs of Poisson points in a position dependent but independent way. We study…
We derive for generally covariant theories the generic dependency of observables on the original fields, corresponding to coordinate-dependent gauge fixings. This gauge choice is equivalent to a choice of intrinsically defined coordinates…
An ensemble of random unistochastic (orthostochastic) matrices is defined by taking squared moduli of elements of random unitary (orthogonal) matrices distributed according to the Haar measure on U(N) (or O(N), respectively). An ensemble of…
Let $X = \{X(t): t\in T \}$ be a non-centered, unit-variance, smooth Gaussian random field indexed on some parameter space $T$, and let $A_u(X,T) = \{t\in T: X(t)\geq u\}$ be the excursion set of $X$ exceeding level $u$. Under certain…
Given a `genus' function $g=g(n)$, we let $\mathcal{E}^g$ be the class of all graphs $G$ such that if $G$ has order $n$ (that is, has $n$ vertices) then it is embeddable in a surface of Euler genus at most $g(n)$. Let the random graph $R_n$…