Related papers: Central limit theorems for high dimensional lattic…

We study $\gamma$-vectors associated with $h^*$-vectors of symmetric edge polytopes both from a deterministic and a probabilistic point of view. On the deterministic side, we prove nonnegativity of $\gamma_2$ for any graph and completely…

In this paper we review the asymptotic matching conjectures for $r$-regular bipartite graphs, and their connections in estimating the monomer-dimer entropies in $d$-dimensional integer lattice and Bethe lattices. We prove new rigorous upper…

Using an averaged generating function for coloured hard-dimers, some random variables of interest are studied. The main result lies in the fact that all their probability distributions obey a central limit theorem.

We compute the canonical form of the cosmological polytope for any graph in terms of the dual of the shifted cosmological polytope in two different ways. On the way, we provide an explicit coordinate description of the dual of the…

Motivated by limits of critical inhomogeneous random graphs, we construct a family of sequences of measured metric spaces that we call continuous multiplicative graphs, that are expected to be the universal limit of graphs related to the…

We study the Central Limit Theorem (CLT) in the so-called mixed (anisotropic) Lebesgue-Riesz spaces and tail behavior of normed sums of centered random independent variables (vectors) with values in these spaces.

We study inhomogeneous random graphs with a finite type space. For a natural generalization of the model as a dynamic network-valued process, the paper establishes the following results: (a) Functional central limit theorems for the…

Mixed level orthogonal arrays are basic structures in experimental design. We develop three algorithms that compute Rao and Gilbert-Varshamov type bounds for mixed level orthogonal arrays. The computational complexity of the terms involved…

A theorem of Scott gives an upper bound for the normalized volume of lattice polygons with exactly $i>0$ interior lattice points. We will show that the same bound is true for the normalized volume of lattice polytopes of degree 2 even in…

We provide a simple proof for of the central limit theorem for the number of vertices in the giant for super-critical stochastic block model using the breadth-first walk of Konarovskyi, Limic and the author (2024). Our approach follows the…

We study the asymptotics of large directed graphs, constrained to have certain densities of edges and/or outward $p$-stars. Our models are close cousins of exponential random graph models (ERGMs), in which edges and certain other subgraph…

Random simplices and more general random convex bodies of dimension $p$ in $\mathbb{R}^n$ with $p\leq n$ are considered, which are generated by random vectors having an elliptical distribution. In the high-dimensional regime, that is, if…

We consider a class of elliptic random matrices which generalize two classical ensembles from random matrix theory: Wigner matrices and random matrices with iid entries. In particular, we establish a central limit theorem for linear…

We prove a central limit theorem for strictly stationary random fields under a sharp projective condition. The assumption was introduced in the setting of random variables by Maxwell and Woodroofe. Our approach is based on new results for…

We consider "randomized" statistics constructed by using a finite number of observations a random field at randomly chosen points. We generalize the invariance principle (the functional CLT), the Glivenko--Cantelli theorem, the theorem…

A Central Limit Theorem is proved for linear random fields when sums are taken over finite disjoint union of rectangles. The approach does not rely upon the use of Beveridge Nelson decomposition and the conditions needed are similar to…

We establish limit theorems that describe the asymptotic local and global geometric behaviour of random enriched trees considered up to symmetry. We apply these general results to random unlabelled weighted rooted graphs and uniform random…

We study random graphs with latent geometric structure, where the probability of each edge depends on the underlying random positions corresponding to the two endpoints. We focus on the setting where this conditional probability is a…

In this paper, we prove a local limit theorem for the distribution of the number of triangles in the Erdos-Renyi random graph $G(n,p)$, where $p \in (0,1)$ is a fixed constant. Our proof is based on bounding the characteristic function…

The theory of graphons comes with a natural sampling procedure, which results in an inhomogeneous variant of the Erd\H{o}s--R\'enyi random graph, called $W$-random graphs. We prove, via the method of moments, a limit theorem for the number…