Related papers: Moderate deviations for the size of the giant comp…
In this paper, we investigate a stochastic approximation procedure $\left(X_n\right)_{n\ge 0}$ taking values in $R$. The process is adapted to a filtration $(F_n)_{n\ge 0}$ and satisfies the recursion…
We characterize the size of the largest common induced subgraph of two independent random uniform $d$-hypergraphs of different sizes with $d\geq 3$. More precisely, its distribution is asymptotically concentrated on two points, and we…
We consider the empirical neighborhood distribution of marked sparse Erd\"os-R\'enyi random graphs, obtained by decorating edges and vertices of a sparse Erd\"os-R\'enyi random graph with i.i.d.\ random elements taking values on Polish…
High-order structures have been recognised as suitable models for systems going beyond the binary relationships for which graph models are appropriate. Despite their importance and surge in research on these structures, their random cases…
In 1998, Molloy and Reed showed that, under suitable conditions, if a sequence of degree sequences converges to a probability distribution $D$, then the size of the largest component in corresponding $n$-vertex random graph is…
Bitseki and Delmas (2021) have studied recently the central limit theorem for kernel estimator of invariant density in bifurcating Markov chains models. We complete their work by proving a moderate deviation principle for this estimator.…
We analyze the dynamics of moderate fluctuations for macroscopic observables of the random field Curie Weiss model (i.e., standard Curie-Weiss model embedded in a site dependent, i.i.d. random environment). We obtain path space large…
We consider preferential attachment random graphs which may be obtained as follows: It starts with a single node. If a new node appears, it is linked by an edge to one or more existing node(s) with a probability proportional to function of…
In this article we find exponential good approximation of the empirical neigbourhood distribution of symbolled random graphs conditioned to a given empirical symbol distribution and empirical pair distribution. Using this approximation we…
We establish a large deviation principle for the smallest eigenvalue of a random matrix model composed of the sum of a GOE matrix and a diagonal matrix with an outlier. Our result generalizes and unifies previously studied cases.
We consider a random geometric graph obtained by placing a Poisson point process of intensity 1 in the d-dimensional torus of side length n^(1/d) and connecting two points by an edge if their distance is at most r. We consider the case of…
We present a novel approach to study the evolution of the size (i.e. the number of vertices) of the giant component of a random graph process. It is based on the exploration algorithm called simultaneous breadth-first walk, introduced by…
We establish a moderate deviations principle (MDP) for the log-determinant $\log | \det (M_n) |$ of a Wigner matrix $M_n$ matching four moments with either the GUE or GOE ensemble. Further we establish Cram\'er--type moderate deviations and…
Consider the random graph sampled uniformly from the set of all simple graphs with a given degree sequence. Under mild conditions on the degrees, we establish a Large Deviation Principle (LDP) for these random graphs, viewed as elements of…
We consider a conditionally Poissonian random graph model where the mean degrees, `capacities', follow a power-tailed distribution with finite mean and infinite variance. Such a graph of size $N$ has a giant component which is super-small…
The upper tail problem in a random graph asks to estimate the probability that the number of copies of some fixed subgraph in an Erd\H{o}s--R\'enyi random graph exceeds its expectation by some constant factor. There has been much exciting…
We introduce the study of \textit{randomly oriented divisor graphs}. For each $\rho \in [0,1]$, the randomly oriented divisor graph $\mathcal{D}_\rho(N)$ is obtained from the divisor graph on $\{1, 2, \ldots, N\}$ by directing each edge…
In this manuscript a unified framework for conducting inference on complex aggregated data in high dimensional settings is proposed. The data are assumed to be a collection of multiple non-Gaussian realizations with underlying undirected…
In this paper we study empirical measures which can be thought as a decoupled version of the empirical measures generated by random matrices. We prove the large deviation principle with the rate function, which is finite only on product…
It is well-known that the behaviour of a random subgraph of a $d$-dimensional hypercube, where we include each edge independently with probability $p$, undergoes a phase transition when $p$ is around $\frac{1}{d}$. More precisely, standard…