Related papers: Limit theorems under heavy-tailed scenario in the …
In this paper, we study fluctuations of conditionally centered statistics of the form $$N^{-1/2}\sum_{i=1}^N c_i(g(\sigma_i)-\mathbb{E}_N[g(\sigma_i)|\sigma_j,j\neq i])$$ where $(\sigma_1,\ldots ,\sigma_N)$ are sampled from a dependent…
In this paper we address the problem of testing whether two observed trees $(t,t')$ are sampled either independently or from a joint distribution under which they are correlated. This problem, which we refer to as correlation detection in…
This paper studies a statistical network model generated by a large number of randomly sized overlapping communities, where any pair of nodes sharing a community is linked with probability $q$ via the community. In the special case with…
We prove uniform convergence results for the integrated periodogram of a weakly dependent time series, namely a law of large numbers and a central limit theorem. These results are applied to Whittle's parametric estimation. Under general…
The dynamics of a rain forest is extremely complex involving births, deaths and growth of trees with complex interactions between trees, animals, climate, and environment. We consider the patterns of recruits (new trees) and dead trees…
In this paper we extend our previous results on the connectivity functions and pressure of the Random Cluster Model in the highly subcritical phase and in the highly supercritical phase, originally proved only on the cubic lattice $\Z^d$,…
We study persistent Betti numbers and persistence diagrams obtained from time series and random fields. It is well known that the persistent Betti function is an efficient descriptor of the topology of a point cloud. So far, convergence…
Motivated by an application in community detection, we consider an \ER random graph conditioned on the rare event that all connected components are fully connected. Such graphs can be considered as partitions of vertices into cliques.…
The threshold network model is a type of finite random graphs. In this paper, we introduce a generalized threshold network model. A pair of vertices with random weights is connected by an edge when real-valued functions of the pair of…
We prove that under an easily verifiable set of conditions a sequence of associated random fields converges under rescaling to the Poisson Point Process and give a couple of examples.
A theorem of Frieze from 1985 asserts that the total weight of the minimum spanning tree of the complete graph $K_n$ whose edges get independent weights from the distribution $UNIFORM[0,1]$ converges to Ap\'ery's constant in probability, as…
This article is a presentation of specific recent results describing scaling limits of individual-based models. Thanks to them, we wish to relate the time-scales typical of demographic dynamics and natural selection to the parameters of the…
For random combinatorial optimization problems, there has been much progress in establishing laws of large numbers and computing limiting constants for the optimal value of various problems. However, there has not been as much success in…
We get central limit type theorems for the total number of edges in the generalized random graphs with random vertex weights under different moment conditions on distributions of the weights.
We establish central limit theorems (CLTs) for the linear spectral statistics of the adjacency matrix of inhomogeneous random graphs across all sparsity regimes, providing explicit covariance formulas under the assumption that the variance…
Geometric scale-free random graphs are popular models for networks that exhibit as heavy-tailed degree distributions, small-worldness and high clustering. In these models, vertices have weights that cause the heavy-tailed degrees and are…
Link prediction systems (e.g. recommender systems) typically use graph topology as one of their main sources of information. However, automorphisms and related properties of graphs beget inherent limits in predictability. We calculate hard…
Statistical inference for exponential-family models of random graphs with dependent edges is challenging. We stress the importance of additional structure and show that additional structure facilitates statistical inference. A simple…
A superprocess limit for an interacting birth-death particle system modelling a population with trait and physical age-structures is established. Traits of newborn offspring are inherited from the parents except when mutations occur, while…
We present here a new and universal approach for the study of random and/or trees, unifying in one framework many different models, including some novel ones not yet understood in the literature. An and/or tree is a Boolean expression…