Related papers: Simple stochastic processes behind Menzerath's Law
The distribution behavior dictated by the Menzerath-Altmann (MA) law is frequently encountered in linguistic and natural organizations at various structural levels. The mathematical form of this empirical law comprises three fitting…
The importance of statistical patterns of language has been debated over decades. Although Zipf's law is perhaps the most popular case, recently, Menzerath's law has begun to be involved. Menzerath's law manifests in language, music and…
Multiplicative random processes in (not necessaryly equilibrium or steady state) stochastic systems with many degrees of freedom lead to Boltzmann distributions when the dynamics is expressed in terms of the logarithm of the normalized…
It is argued that the present log-normal distribution of language sizes is, to a large extent, a consequence of demographic dynamics within the population of speakers of each language. A two-parameter stochastic multiplicative process is…
Human history leaves fingerprints in human languages. Little is known over language evolution and its study is of great importance. Here, we construct a simple stochastic model and compare its results to statistical data of real languages.…
We investigate the origin of Zipf's law for words in written texts by means of a stochastic dynamical model for text generation. The model incorporates both features related to the general structure of languages and memory effects inherent…
Stochastic averaging allows for the reduction of the dimension and complexity of stochastic dynamical systems with multiple time scales, replacing fast variables with statistically equivalent stochastic processes in order to analyze…
We explain Kossovsky's generalization of Benford's law which is a formula that approximates the distribution of leftmost digits in finite sequences of natural data and apply it to six sequences of data including populations of US cities and…
Statistical laws describe regular patterns observed in diverse scientific domains, ranging from the magnitude of earthquakes (Gutenberg-Richter law) and metabolic rates in organisms (Kleiber's law), to the frequency distribution of words in…
An important body of quantitative linguistics is constituted by a series of statistical laws about language usage. Despite the importance of these linguistic laws, some of them are poorly formulated, and, more importantly, there is no…
Traditional linguistic theories have largely regard language as a formal system composed of rigid rules. However, their failures in processing real language, the recent successes in statistical natural language processing, and the findings…
Zipf's law is just one out of many universal laws proposed to describe statistical regularities in language. Here we review and critically discuss how these laws can be statistically interpreted, fitted, and tested (falsified). The modern…
In this paper, we study the asymptotic behavior of a fully-coupled slow-fast McKean-Vlasov stochastic system. Using the non-linear Poisson equation on Wasserstein space, we first establish the strong convergence in the averaging principle…
We analyse correspondence of a text to a simple probabilistic model. The model assumes that the words are selected independently from an infinite dictionary. The probability distribution correspond to the Zipf---Mandelbrot law. We count…
In this paper we combine statistical analysis of large text databases and simple stochastic models to explain the appearance of scaling laws in the statistics of word frequencies. Besides the sublinear scaling of the vocabulary size with…
Present human languages display slightly asymmetric log-normal (Gauss) distribution for size [1-3], whereas present cities follow power law (Pareto-Zipf law)[4]. Our model considers the competition between languages and that between cities…
The dependence with text length of the statistical properties of word occurrences has long been considered a severe limitation quantitative linguistics. We propose a simple scaling form for the distribution of absolute word frequencies…
In this paper the Zipf-Mandelbrot law is revisited in the context of linguistics. Despite its widespread popularity the Zipf--Mandelbrot law can only describe the statistical behaviour of a rather restricted fraction of the total number of…
We study a stochastic model based on a modified fragmentation of a finite interval. The mechanism consists in cutting the interval at a random location and substituting a unique fragment on the right of the cut to regenerate and preserve…
Many studies in Economics and other disciplines have been reporting distributions following power-law behavior (i.e distributions of incomes (Pareto's law), city sizes (Zipf's law), frequencies of words in long sequences of text etc.)[1, 6,…