Related papers: Some Refinements of Large Deviation Tail Probabili…
Multivariate regular variation plays a role assessing tail risk in diverse applications such as finance, telecommunications, insurance and environmental science. The classical theory, being based on an asymptotic model, sometimes leads to…
We obtain asymptotic approximations for the probability density function of the product of two correlated normal random variables with non-zero means and arbitrary variances. As a consequence, we deduce asymptotic approximations for the…
We establish the one-to one bilateral interrelations between an asymptotic behavior for the tail of distributions for random variables and its great moments evaluation. Our results generalize the famous Richter's ones.
This work prepares new probability bounds for sums of random, independent, Hermitian tensors. These probability bounds characterize large-deviation behavior of the extreme eigenvalue of the sums of random tensors. We extend Lapalace…
Given an arbitrary continuous probability density function, it is introduced a conjugated probability density, which is defined through the Shannon information associated with its cumulative distribution function. These new densities are…
Large deviation principles and related results are given for a class of Markov chains associated to the "leaves" in random recursive trees and preferential attachment random graphs, as well as the "cherries" in Yule trees. In particular,…
We derive the tail inequalities between two random variables starting from inequalities between its moment, or more generally between its Lebesgue-Riesz norms, which holds true on certain sets of parameters. We consider some applications…
Posterior computation for high-dimensional data with many parameters can be challenging. This article focuses on a new method for approximating posterior distributions of a low- to moderate-dimensional parameter in the presence of a…
We study numerically the distributions of the length $L$ of the longest increasing subsequence (LIS) for the two cases of random permutations and of one-dimensional random walks. Using sophisticated large-deviation algorithms, we are able…
We revisit and refine known tail inequalities and confidence bounds for the hypergeometric distribution, i.e., for the setting where we sample without replacement from a fixed population with binary values or properties. The results are…
We obtain sharp large deviation estimates for exceedance probabilities in dependent triangular array threshold models with a diverging number of latent factors. The prefactors quantify how latent-factor dependence and tail geometry enter at…
Suppose that $X$ is a bounded-degree polynomial with nonnegative coefficients on the $p$-biased discrete hypercube. Our main result gives sharp estimates on the logarithmic upper tail probability of $X$ whenever an associated extremal…
We study the upper tail of the number of arithmetic progressions of a given length in a random subset of {1,...,n}, establishing exponential bounds which are best possible up to constant factors in the exponent. The proof also extends to…
We show an extension of Sanov's theorem on large deviations, controlling the tail probabilities of i.i.d. random variables with matching concentration and anti-concentration bounds. This result has a general scope, applies to samples of any…
A particular direction of recent advance about stochastic deep-learning algorithms has been about uncovering a rather mysterious heavy-tailed nature of the stationary distribution of these algorithms, even when the data distribution is not…
Normalizing flows are a flexible class of probability distributions, expressed as transformations of a simple base distribution. A limitation of standard normalizing flows is representing distributions with heavy tails, which arise in…
We study persistence probabilities for random walks in correlated Gaussian random environment first studied by Oshanin, Rosso and Schehr. From the persistence results, we can deduce properties of critical branching processes with offspring…
Measures of tail dependence between random variables aim to numerically quantify the degree of association between their extreme realizations. Existing tail dependence coefficients (TDCs) are based on an asymptotic analysis of relevant…
Approximating complex probability distributions, such as Bayesian posterior distributions, is of central interest in many applications. We study the expressivity of geometric Gaussian approximations. These consist of approximations by…
We investigate asymptotic behaviour of probabilities of large deviations for normalized combinatorial sums. We find a zone in which these probabilities are equivalent to the tail of the standard normal law. Our conditions are similar to the…