Zipf’s law of word frequencies for language discourses is established with statistical rigor. Data show a departure from Zipf’s power law term at low frequencies. This is accounted by a modifying exponential term. Both arise naturally in a model for word frequencies based on Information Theory, algorithmic coding of a text preserving the symbol sequence, concepts from quantum statistical physic...

Zipf's law governs many features of the Internet. Observations of Zipf distributions, while interesting in and of themselves, have strong implications for the design and function of the Internet. The connectivity of Internet routers influences the robustness of the network while the distribution in the number of email contacts affects the spread of email viruses. Even web caching strategies are...

Despite more than thirty years of intensive research efforts, textual passwords are still enveloped in mysterious veils. In this work, we make a substantial step forward in understanding the underlying distributions of passwords. By conducting linear regressions on a corpus of 97.2 million passwords (a mass of chaotic data), we for the first time show that Zipf ’s law perfectly exists in user-g...

We propose models for data authentication which take into account the behavior of the clients who perform queries. Our models reduce the size of the authenticated proof when the frequency of the query corresponding to a given data is higher. Existing models implicitly assume the frequency distribution of queries to be uniform, but in reality, this distribution generally follows Zipf’s law. Our ...

This paper studies concentration (i.e. inequality) aspects of the functions of Zipf and of Lotka. Since both functions are power laws (i.e. they are – mathematically the same) it suffices to develop one concentration theory for power laws and apply it twice for the different interpretations of the laws of Zipf and Lotka. After a brief repetition of the functional relationships between Zipf’s la...

In this paper we show how the Shannon entropy is connected to the theory of majorization. They are both linked to the measure of disorder in a system. However, the theory of majorization usually gives stronger criteria than the entropic inequalities. We give some generalized results for majorization inequality using Csiszár f-divergence. This divergence, applied to some special convex functions...