Related papers: Moderate deviations in random graphs and Bernoulli…

The methods of non-homogeneous random graphs calibration are developed for social networks simulation. The graphs are calibrated by the degree distributions of the vertices and the edges. The mathematical foundation of the methods is formed…

We prove a general theorem to bound the total variation distance between the distribution of an integer valued random variable of interest and an appropriate discretized normal distribution. We apply the theorem to 2-runs in a sequence of…

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…

In this paper we derive the moderate deviation principle for stationary sequences of bounded random variables under martingale-type conditions. Applications to functions of $\phi$-mixing sequences, contracting Markov chains, expanding maps…

In this paper, we derive the moderate deviation principle for stationary sequences of bounded random variables with values in a Hilbert space. The conditions obtained are expressed in terms of martingale-type conditions. The main tools are…

We study the spectrum of adjacency matrices of random graphs. We develop two techniques to lower bound the mass of the continuous part of the spectral measure or the density of states. As an application, we prove that the spectral measure…

Inspired by the recent work [MRT21], we prove a non-universal non-central Moderate Deviation principle for the nodal length of arithmetic random waves (Gaussian Laplace eigenfunctions on the standard flat torus) both on the whole manifold…

We give a simple, computationally efficient, and node-differentially-private algorithm for estimating the parameter of an Erdos-Renyi graph---that is, estimating p in a G(n,p)---with near-optimal accuracy. Our algorithm nearly matches the…

One of the first steps in applications of statistical network analysis is frequently to produce summary charts of important features of the network. Many of these features take the form of sequences of graph statistics counting the number…

Distributed consensus computation over random graph processes is considered. The random graph process is defined as a sequence of random variables which take values from the set of all possible digraphs over the node set. At each time step,…

Importance sampling has become an important tool for the computation of tail-based risk measures. Since such quantities are often determined mainly by rare events standard Monte Carlo can be inefficient and importance sampling provides a…

We consider (annealed) large deviation principles for component empirical measures of several families of marked sparse random graphs, including (i) uniform graphs on $n$ vertices with a fixed degree distribution; (ii) uniform graphs on $n$…

In this paper, we study large and moderate deviation principles for stochastic partial differential equations (SPDEs) on metric graphs and their associated multiscale models via the weak convergence approach, providing a refined…

We calculate a Ricci curvature lower bound for some classical examples of random walks, namely, a chain on a slice of the n-dimensional discrete cube (the so-called Bernoulli-Laplace model) and the random transposition shuffle of the…

Sequential change-point detection for graphs is a fundamental problem for streaming network data types and has wide applications in social networks and power systems. Given fixed vertices and a sequence of random graphs, the objective is to…

We consider the multi-parameter random simplicial complex as a higher dimensional extension of the classical Erd\"os-R\'enyi graph. We investigate appearance of "unusual" topological structures in the complex from the point of view of large…

This work introduces the minimax Laplace transform method, a modification of the cumulant-based matrix Laplace transform method developed in "User-friendly tail bounds for sums of random matrices" (arXiv:1004.4389v6) that yields both upper…

In this paper we obtain a Bernstein type inequality for a class of weakly dependent and bounded random variables. The proofs lead to a moderate deviations principle for sums of bounded random variables with exponential decay of the strong…

Network analysis has become an increasingly prevalent research tool across a vast range of scientific fields. Here, we focus on the particular issue of comparing network statistics, i.e. graph-level measures of network structural features,…

We define a class of continuous graded graphs similar to the graph of Gelfand--Tsetlin patterns, and describe the set of all ergodic central measures of discrete type on the path spaces of such graphs. The main observation is that an…