Related papers: Moderate deviations for the size of the giant comp…

The phase transition in the size of the giant component in random graphs is one of the most well-studied phenomena in random graph theory. For hypergraphs, there are many possible generalisations of the notion of a component, and for all…

The term moderate deviations is often used in the literature to mean a class of large deviation principles that, in some sense, fills the gap between a convergence in probability of some random variables to a constant and a weak convergence…

We consider the random geometric graph on $n$ vertices drawn uniformly from a $d$--dimensional sphere. We focus on the sparse regime, when the expected degree is constant independent of $d$ and $n$. We show that, when $d$ is larger than $n$…

The Erd\H{o}s-Kac theorem is a celebrated result in number theory which says that the number of distinct prime factors of a uniformly chosen random integer satisfies a central limit theorem. In this paper, we establish the large deviations…

The $N$ vertices of a quantum random graph are each a circle independently punctured at Poisson points of arrivals, with parallel connections derived through for each pair of these punctured circles by yet another independent Poisson…

In this paper, moderate deviations for normal approximation of functionals over infinitely many Rademacher random variables are derived. They are based on a bound for the Kolmogorov distance between a general Rademacher functional and a…

We equip the edges of a deterministic graph $H$ with independent but not necessarily identically distributed weights and study a generalized version of matchings (i.e. a set of vertex disjoint edges) in $H$ satisfying the property that…

We establish a moderate deviation principle (MDP) for the number of eigenvalues of a Wigner matrix in an interval. The proof relies on fine asymptotics of the variance of the eigenvalue counting function of GUE matrices due to Gustavsson.…

For the Erd\H{o}s-R\'enyi random graph G(n,p), we give a precise asymptotic formula for the size of a largest vertex subset in G(n,p) that induces a subgraph with average degree at most t, provided that p = p(n) is not too small and t =…

We establish a moderate deviation principle (MDP) for the number of eigenvalues of a Wigner matrix in an interval close to the edge of the spectrum. Moreover we prove a MDP for the $i$th largest eigenvalue close to the edge. The proof…

The $W$-random graphs provide a flexible framework for modeling large random networks. Using the Large Deviation Principle (LDP) for $W$-random graphs from [9], we prove the LDP for the corresponding class of random symmetric…

A sequence $D = \{d_1,...d_n\}$ is a feasible degree sequence if there is a graph on $\{1,...,n\}$ such that $i$ has degree $d_i$. For such a sequence, $G(D)$ is a graph chosen uniformly at random from those with the given degree sequence.…

We study the greedy independent set algorithm on sparse Erd\H{o}s-R\'enyi random graphs ${\mathcal G}(n,c/n)$. This range of $p$ is of interest due to the threshold at $c=e$, beyond which it appears that greedy algorithms are affected by a…

We consider a class of particle systems described by differential equations (both stochastic and deterministic), in which the interaction network is determined by the realization of an Erd\H{o}s-R\'enyi graph with parameter $p_n\in (0, 1]$,…

We establish a moderate deviation principle for the maximum likelihood estimator of the four parameters of a geometrically ergodic Heston process. We also obtain moderate deviations for the maximum likelihood estimator of the couple of…

We study the exploration of an Erd\"os-R\'enyi random graph by a respondent-driven sampling method, where discovered vertices reveal their neighbours. Some of them receive coupons to reveal in their turn their own neighbourhood. This leads…

Much work in the study of large deviations for random graph models is focused on the dense regime where the theory of graphons has emerged as a principal tool. These tools do not give a good approach to large deviation problems for random…

In [Amir et al.], the authors consider the generalization $\Gor$ of the Erd\H{o}s-R\'enyi random graph process $G$, where instead of adding new edges uniformly, $\Gor$ gives a weight of size 1 to missing edges between pairs of isolated…

Ewens-Pitman model has been successfully applied to various fields including Bayesian statistics. There are four important estimators $K_{n},M_{l,n}$,$K_{m}^{(n)},M_{l,m}^{(n)}$. In particular, $M_{1,n}, M_{1,m}^{(n)}$ are related to…

We present a large-deviations/thermodynamic approach to the classic problem of percolation on the complete graph. Specifically, we determine the large-deviation rate function for the probability that the giant component occupies a fixed…