Related papers: Large deviations for random projections of $\ell^p…

We prove a large deviation principle for the point process of large Poisson $k$-nearest neighbor balls in hyperbolic space. More precisely, we consider a stationary Poisson point process of unit intensity in a growing sampling window in…

We prove a Large Deviation Principle for the random spec- tral measure associated to the pair $(H_N; e)$ where $H_N$ is sampled in the GUE(N) and e is a fixed unit vector (and more generally in the $\beta$- extension of this model). The…

This short note provides a large-deviation-based upper bound on the growth rate of directed last passage percolation (LPP) using the entropy of the normalized direction vector.

Central limit theorems for the log-volume of a class of random convex bodies in $\mathbb{R}^n$ are obtained in the high-dimensional regime, that is, as $n\to\infty$. In particular, the case of random simplices pinned at the origin and…

In this paper, we first provide a criterion on uniform large deviation principles (ULDP) of stochastic differential equations under Lyapunov conditions on the coefficients, which can be applied to stochastic systems with coefficients of…

We prove a large deviations principle for the total spin and the number of edges under the annealed Ising measure on generalized random graphs. We also give detailed results on how the annealing over the Ising model changes the degrees of…

We study large deviations for some non-local parabolic type equations. We show that, under some assumptions on the non-local term, problems defined in a bounded domain converge with an exponential rate to the solution of the problem defined…

We prove by counterexample that a large deviation principle established by Chen and Feng [{\em Comm. Statist. Theory Methods} {\bf 45} (2016), 400--412] in the framework of sublinear expectations is incorrect. That implies that the rate…

We consider the problem of computing the (two-sided) Hausdorff distance between the unit $\ell_{p_{1}}$ and $\ell_{p_{2}}$ norm balls in finite dimensional Euclidean space for $1 \leq p_1 < p_2 \leq \infty$, and derive a closed-form formula…

In \cite{FTD1}, we proved the almost sure convergence of eigenvalues of the SYK model, which can be viewed as a type of \emph{law of large numbers} in probability theory; in \cite{FTD2}, we proved that the linear statistic of eigenvalues…

In this paper, we show that the basic results in large deviations theory hold for general monetary risk measures, which satisfy the crucial property of max-stability. A max-stable monetary risk measure fulfills a lattice homomorphism…

This paper derives central limit and bootstrap theorems for probabilities that sums of centered high-dimensional random vectors hit hyperrectangles and sparsely convex sets. Specifically, we derive Gaussian and bootstrap approximations for…

We initiate a study of large deviations for block model random graphs in the dense regime. Following Chatterjee-Varadhan(2011), we establish an LDP for dense block models, viewed as random graphons. As an application of our result, we study…

This paper is concerned with the general theme of relating the Large Deviation Principle (LDP) for the invariant measures of stochastic processes to the associated sample path LDP. It is shown that if the sample path deviation function…

We provide rates of convergence in the central limit theorem in terms of projective criteria for adapted stationary sequences of centered random variables taking values in Banach spaces, with finite moment of order $p \in ]2,3]$ as soon as…

We obtain dimension-free concentration inequalities for $\ell^p$-norms, $p\geq2$, of infinitely divisible random vectors with independent coordinates and finite exponential moments. Besides such norms, the methods and results extend to some…

The variance conjecture in Asymptotic Convex Geometry stipulates that the Euclidean norm of a random vector uniformly distributed in a (properly normalised) high-dimensional convex body $K\subset {\mathbb R}^n$ satisfies a Poincar\'e-type…

In this work we determine a process-level Large Deviation Principle (LDP) for a model of interacting particles indexed by a lattice $\mathbb{Z}^d$. The connections are random, sparse and unscaled, so that the system converges in the large…

Consider the standard, one dimensional, nonlinear filtering problem for a diffusion processe $\Xi_t$ observed in small additive white noise. Denote by $q^\epsilon_1(\cdot)$ the density of the law of $\Xi_1$ conditioned on…

Study of the KPZ universality class has seen the emergence of universal objects over the past decade which arise as the scaling limit of the member models. One such object is the directed landscape, and it is known that exactly solvable…