Related papers: Zipf's law in Nuclear Multifragmentation and Perco…
We summarize a book under publication with his title written by the three present authors, on the theory of Zipf's law, and more generally of power laws, driven by the mechanism of proportional growth. The preprint is available upon request…
A prescription for the fragment size distribution resulting from dust grain collisions is essential when modelling a range of astrophysical systems, such as debris disks and planetary rings. While the slope of the fragment size distribution…
Thermodynamical properties of nuclear matter undergoing multifragmentation are studied within a simplified version of the statistical model. An exact analytical solution has been found for the grand canonical ensemble. Excluded volume…
The large body of experimental data on nuclear fission is analyzed with a semi-empirical ordering scheme based on the macro-microscopic approach and the separability of compound-nucleus and fragment properties on the fission path. We apply…
To date, the magnetic structure of nuclei has been poorly constrained, with limited information on its spatial distribution. In this work, we address the composition and distribution of nuclear magnetization in a precision study of…
Utilizing a partitioning method based on equal (or unequal) probabilities -- without incorporating the alpha-cluster ($\alpha$-cluster) model -- allows for the derivation of diverse topological configurations of nuclear fragments resulting…
Using a maximum entropy principle to assign a statistical weight to any graph, we introduce a model of random graphs with arbitrary degree distribution in the framework of standard statistical mechanics. We compute the free energy and the…
We found that in transition arrays of complex atomic spectra, the strengths of electric-dipolar lines obey Benford's law, which means that their significant digits follow a logarithmic distribution favoring the smallest values. This…
We study Bernoulli bond percolation on a random recursive tree of size $n$ with percolation parameter $p(n)$ converging to $1$ as $n$ tends to infinity. The sizes of the percolation clusters are naturally stored in a tree. We prove…
We study intersection properties of two or more independent tree-like random graphs. Our setting encompasses critical, possibly long range, Bernoulli percolation clusters, incipient infinite clusters, as well as critical branching random…
Power law distributions characterise several natural and social phenomena. The Zipf law for cities is one of those. The study views the question of whether that global regularity is independent of different spatial distributions of cities.…
Tokenization is a fundamental step in natural language processing (NLP) and other sequence modeling domains, where the choice of vocabulary size significantly impacts model performance. Despite its importance, selecting an optimal…
In this article, I conduct a textual and contextual analysis of the empirical literature on Zipf's law for cities. Building on previous meta-analysis material openly available, I collect full texts and bibliographies of 66 scientific…
We consider the model of random trees introduced by Devroye (1999), the so-called random split trees. The model encompasses many important randomized algorithms and data structures. We then perform supercritical Bernoulli bond-percolation…
The derivation of the maximum entropy distribution of particles in boxes yields two kinds of distributions: a "bell-like" distribution and a long-tail distribution. The first one is obtained when the ratio between particles and boxes is…
For words, rank-frequency distributions have long been heralded for adherence to a potentially-universal phenomenon known as Zipf's law. The hypothetical form of this empirical phenomenon was refined by Ben\^{i}ot Mandelbrot to that which…
The site percolation problem is one of the core topics in statistical physics. Evaluation of the percolation threshold, which separates two phases (sometimes described as conducting and insulating), is useful for a range of problems from…
We present empirical data on frequency and pattern of misprints in citations to twelve high-profile papers. We find that the distribution of misprints, ranked by frequency of their repetition, follows Zipf's law. We propose a stochastic…
In this paper we derive the maximum entropy characteristics of a particular rank order distribution, namely the discrete generalized beta distribution, which has recently been observed to be extremely useful in modelling many several…
We investigate the maximal non-critical cluster in a big box in various percolation-type models. We investigate its typical size, and the fluctuations around this typical size. The limit law of these fluctuations are related to maxima of…