Related papers: Mod-phi convergence I: Normality zones and precise…
In this paper, we relate the framework of mod-$\phi$ convergence to the construction of approximation schemes for lattice-distributed random variables. The point of view taken here is that of Fourier analysis in the Wiener algebra, allowing…
We prove local limit theorems for mod-{\phi} convergent sequences of random variables, {\phi} being a stable distribution. In particular, we give two new proofs of a local limit theorem in the framework of mod-phi convergence: one proof…
In this paper, we show how to use the framework of mod-Gaussian convergence in order to study the fluctuations of certain models of random graphs, of random permutations and of random integer partitions. We prove that, in these three…
In this paper, we give estimates for the speed of convergence towards a limiting stable law in the recently introduced setting of mod-$\phi$ convergence. Namely, we define a notion of zone of control, closely related to mod-$\phi$…
The purpose of the present paper is to establish moderate deviation principles for a rather general class of random variables fulfilling certain bounds of the cumulants. We apply a celebrated lemma of the theory of large deviations…
We provide a convergence result for sequences of random variables taking values in a metric space that satisfy a stochastic quasi-Fej\'er monotonicity condition, in the context of a (local) compactness assumption. Our result is quantitative…
Density-wave instabilities have been observed and studied in a multitude of materials. Most recently, in the context of unconventional superconductors like the iron-based superconductors, they have excited considerable interest. We analyze…
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…
This paper investigates Frequentist consistency properties of the posterior distributions constructed via Generalized Variational Inference (GVI). A number of generic and novel strategies are given for proving consistency, relying on the…
We use a new method via $p$-Wasserstein bounds to prove Cram\'er-type moderate deviations in (multivariate) normal approximations. In the classical setting that $W$ is a standardized sum of $n$ independent and identically distributed…
In this paper, we study precise deviations including precise large deviations and moderate deviations for discrete marked Hawkes processes for large time asymptotics by using mod-$\phi$ convergence theory.
We establish large deviations properties valid for almost every sample path of a class of stationary mixing processes $(X_1,..., X_n,...)$. These properties are inherited from those of $S_n=\sum_{i=1}^nX_i$ and describe how the local…
In first-passage percolation (FPP), one assigns i.i.d.~weights to the edges of the cubic lattice $\mathbb{Z}^d$ and analyzes the induced weighted graph metric. If $T(x,y)$ is the distance between vertices $x$ and $y$, then a primary…
The purpose of the present paper is to establish explicit bounds on moderate deviation probabilities for a rather general class of geometric functionals enjoying the stabilization property, under Poisson input and the assumption of a…
In this paper, we study the fluctuations of observables of metric measure spaces which are random discrete approximations $X_n$ of a fixed arbitrary (complete, separable) metric measure space $X=(\mathcal{X},d,\mu)$. These observables…
We present several refinements on the fluctuations of sequences of random vectors (with values in the Euclidean space $\mathbb{R}^d$) which converge after normalization to a multidimensional Gaussian distribution. More precisely we refine…
In this paper, we investigate the precise local large deviation probabilities for random sums of independent real-valued random variables with a common distribution $F$, where $F(x+\Delta)=F((x, x+T])$ is an $\mathcal{O}$-regularly varying…
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…
The approximation of a general $d$-variate function $f$ by the shifts $\phi(\cdot-\xi)$, $\xi\in\Xi\subset \Rd$, of a fixed function $\phi$ occurs in many applications such as data fitting, neural networks, and learning theory. When…
Consider the Erd\H{o}s-Renyi random graph on n vertices where each edge is present independently with probability c/n, with c>0 fixed. For large n, a typical random graph locally behaves like a Galton-Watson tree with Poisson offspring…