Related papers: Tail universalities in rank distributions as an al…
We investigate how leaders emerge as a consequence of the competitive dynamics between coupled papers in a model citation network. Every paper is allocated an initial fitness depending on its intrinsic quality. Its fitness then evolves…
Identifying the generating mechanism of a network is challenging as, more often than not, only snapshots are available, but not the full evolution. One candidate for the generating mechanism is preferential attachment which, in its simplest…
We examine random variables in the power law/regularly varying class with stochastic tail exponent, the exponent $\alpha$ having its own distribution. We show the effect of stochasticity of $\alpha$ on the expectation and higher moments of…
An exact solution is presented to a model that mimics the crowding effect in financial markets which arises when groups of agents share information. We show that the size distribution of groups of agents has a power law tail with an…
Strong anomalous diffusion is {often} characterized by a piecewise-linear spectrum of the moments of displacement. The spectrum is characterized by slopes $\xi$ and $\zeta$ for small and large moments, respectively, and by the critical…
For many optimization algorithms the time-to-solution depends not only on the problem size but also on the specific problem instance and may vary by many orders of magnitude. It is then necessary to investigate the full distribution and…
(The third edition corrects minor typos and adds 3 chapters synthesized from published papers plus an appendix on maximum entropy distributions.) The monograph investigates the misapplication of conventional statistical techniques to fat…
Zipf's law is the most common statistical distribution displaying scaling behavior. Cities, populations or firms are just examples of this seemingly universal law. Although many different models have been proposed, no general theoretical…
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 propose a multivariate generative model to capture the complex dependence structure often encountered in business and financial data. Our model features heterogeneous and asymmetric tail dependence between all pairs of individual…
Recent works have highlighted optimization difficulties faced by gradient descent in training the first and last layers of transformer-based language models, which are overcome by optimizers such as Adam. These works suggest that the…
The so-called partition function is a sample moment statistic based on blocks of data and it is often used in the context of multifractal processes. It will be shown that its behaviour is strongly influenced by the tail of the distribution…
We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling…
In a range of citation networks, the in-degree distributions boast time-periodicity---the distributions of citations per article published each year present similar scale-free tails. This phenomenon can be regarded as a consequence of the…
We reconsider a classical, well-studied problem from applied probability. This is the max-sum equivalence of randomly weighted sums, and the originality is because we manage to include interdependence among the primary random variables, as…
This article describes mathematical methods for estimating the top-tail of the wealth distribution and therefrom the share of total wealth that the richest $p$ percent hold, which is an intuitive measure of inequality. As the data base for…
The total number of fatalities of an epidemic outbreak is a dramatic but extremely informative quantity. Knowledge of the statistics of this quantity allows the calculation of the mean total number of fatalities conditioned to the fact that…
Here we present a new class of optimality for coding systems. Members of that class are displaced linearly from optimal coding and thus exhibit Zipf's law, namely a power-law distribution of frequency ranks. Within that class, Zipf's law,…
We investigate the use of optimization to compute bounds for extremal performance measures. This approach takes a non-parametric viewpoint that aims to alleviate the issue of model misspecification possibly encountered by conventional…
Accurate goodness-of-fit tests for the extreme tails of empirical distributions is a very important issue, relevant in many contexts, including geophysics, insurance, and finance. We have derived exact asymptotic results for a…