Related papers: Where Do Thin Tails Come From?

We study the problems related to the estimation of the Gini index in presence of a fat-tailed data generating process, i.e. one in the stable distribution class with finite mean but infinite variance (i.e. with tail index $\alpha\in(1,2)$).…

Despite the successes of probabilistic models based on passing noise through neural networks, recent work has identified that such methods often fail to capture tail behavior accurately, unless the tails of the base distribution are…

We discuss non-Gaussian random matrices whose elements are random variables with heavy-tailed probability distributions. In probability theory heavy tails of the distributions describe rare but violent events which usually have dominant…

We analyze quantitatively the effect of spurious multifractality induced by the presence of fat-tailed symmetric and asymmetric probability distributions of fluctuations in time series. In the presented approach different kinds of symmetric…

This is a continuation of our earlier work [Stochastic Processes and their Applications, 129(1), pp.102--128, 2019] on the random walk in random scenery and in random layered conductance. We complete the picture of upper deviation of the…

Motivated by the empirical observation of power-law distributions in the credits (e.g., ``likes'') of viral posts in social media, we introduce a high-dimensional tail index regression model and propose methods for estimation and inference…

This article is devoted to the study of tail index estimation based on i.i.d. multivariate observations, drawn from a standard heavy-tailed distribution, i.e. of which 1-d Pareto-like marginals share the same tail index. A multivariate…

I start by reviewing some basic properties of random graphs. I then consider the role of random walks in complex networks and show how they may be used to explain why so many long tailed distributions are found in real data sets. The key…

It is known that large deviations of sums of subexponential random variables are most likely realised by deviations of a single random variable. In this article we give a detailed picture of how subexponential random variables are…

We establish the large deviation probabilities for the height of random recursive trees, revealing polynomial upper-tail decay and stretched-exponential lower-tail decay. Remarkably, the lower tail features an atypical prefactor that grows…

We obtain first decay rates of probabilities of tails of multivariate polynomials built on independent random variables with heavy tails. Then we derive stable limit theorems for nonconventional sums of the form $\sum_{Nt\geq n\geq…

The paper suggests a simple method of deriving minimax lower bounds to the accuracy of statistical inference on heavy tails. A well-known result by Hall and Welsh (Ann. Statist. 12 (1984) 1079-1084) states that if $\hat{\alpha}_n$ is an…

In this note we prove bounds on the upper and lower probability tails of sums of independent geometric or exponentially distributed random variables. We also prove negative results showing that our established tail bounds are asymptotically…

Consider the linear nonhomogeneous fixed point equation R =_d sum_{i=1}^N C_i R_i + Q, where (Q,N,C_1,...,C_N) is a random vector with N in{0,1,2,3,...}U{infty}, {C_i}_{i=1}^N >= 0, P(|Q|>0) > 0, and {R_i}_{i=1}^N is a sequence of i.i.d.…

We present an overview of possible reasons for the appearance of heavy-tailed distributions in applications to the natural sciences. These distributions include the laws of Pareto, Lotka, and some new ones. The reasons are illustrated using…

Heavy-tailed distributions are frequently used to enhance the robustness of regression and classification methods to outliers in output space. Often, however, we are confronted with "outliers" in input space, which are isolated observations…

Paths are important structural elements in complex networks because they are finite (unlike walks), related to effective node coverage (minimum spanning trees), and can be understood as being dual to star connectivity. This article…

We study large deviation probabilities for a sum of dependent random variables from a heavy-tailed factor model, assuming that the components are regularly varying. We identify conditions where both the factor and the idiosyncratic terms…

Multivariate rapid variation describes decay rates of joint light tails of a multivariate distribution. We impose a local uniformity condition to control decay variation of distribution tails along different directions, and using…

We present a simple model of a stock market where a random communication structure between agents gives rise to a heavy tails in the distribution of stock price variations in the form of an exponentially truncated power-law, similar to…