相关论文: Relating Turing's Formula and Zipf's Law

As the most fundamental empirical law, Zipf's law has been studied from many aspects. But its meaning is still an open problem. Some models have been constructed to explain Zipf's law. In the letter, a new concept named nonsymmetric entropy…

Turing's estimator allows one to estimate the probabilities of outcomes that either do not appear or only rarely appear in a given random sample. We perform a simulation study to understand the finite sample performance of several related…

We recently introduced a robust approach to the derivation of sharp asymptotic formula for correlation functions of statistical mechanics models in the high-temperature regime. We describe its application to the nonperturbative proof of…

Stirling numbers of the first kind are common in number theory and combinatorics; through Ewen's sampling formula, these numbers enter into the calculation of several population genetics statistics, such as Fu's Fs. In previous papers we…

In this article we study asymptotic properties of weighted samples produced by the auxiliary particle filter (APF) proposed by pitt and shephard (1999). Besides establishing a central limit theorem (CLT) for smoothed particle estimates, we…

We introduce a simple and generic model that reproduces Zipf's law. By regarding the time evolution of the model as a random walk in the logarithmic scale, we explain theoretically why this model reproduces Zipf's law. The explanation shows…

Zipf's law in language lacks a definitive origin, debated across fields. This study explains Zipf-like behavior using geometric mechanisms without linguistic elements. The Full Combinatorial Word Model (FCWM) forms words from a finite…

The localized eigenstates of the Harper equation exhibit universal self-similar fluctuations once the exponentially decaying part of a wave function is factorized out. For a fixed quantum state, we show that the whole localized phase is…

In this paper, we show how to estimate the asymptotic (conditional) covariance matrix, which appears in central limit theorems in high-frequency estimation of asset return volatility. We provide a recipe for the estimation of this matrix by…

Sharp, nonasymptotic bounds are obtained for the relative entropy between the distributions of sampling with and without replacement from an urn with balls of $c\geq 2$ colors. Our bounds are asymptotically tight in certain regimes and,…

The population $\mathrm{KL}_{\inf}$ is a fundamental quantity that appears in lower bounds for (asymptotically) optimal regret of pure-exploration stochastic bandit algorithms, and optimal stopping time of sequential tests. Motivated by…

In this article, we provide a comprehensive analysis of the asymptotic behavior of Bell numbers, enhancing and unifying various results previously dispersed in the literature. We establish several explicit lower and upper bounds. The main…

Two new test statistics are introduced to test the null hypotheses that the sampling distribution has an increasing hazard rate on a specified interval [0,a]. These statistics are empirical L_1-type distances between the isotonic estimates,…

In this paper the perturbation theory with the frequency of transition in atom as perturbation parameter is constructed. The estimation of the reminder term of series of this perturbation theory is given. With the help of this perturbation…

After having shown that the formula which describes the Doppler effect in the general case holds only in the case of the "very high" frequency assumption, we derive free of assumptions Doppler formulas for two scenarios presented in the…

Why does Zipf's law give a good description of data from seemingly completely unrelated phenomena? Here it is argued that the reason is that they can all be described as outcomes of a ubiquitous random group division: the elements can be…

We analyse the Dirichlet convolution ring of arithmetic number theoretic functions. It turns out to fail to be a Hopf algebra on the diagonal, due to the lack of complete multiplicativity of the product and coproduct. A related Hopf algebra…

We present a technique to study normalizing strategies when termination is asymptotic, that is, it appears as a limit, as opposite to reaching a normal form in a finite number of steps. Asymptotic termination occurs in several settings,…

The rate coding response of a single peripheral sensory neuron in the asymptotic, near-equilibrium limit can be derived using information theory, asymptotic Bayesian statistics and a theory of complex systems. Almost no biological knowledge…

Zipf's power law is a general empirical regularity found in many natural and social systems. A recently developed theory predicts that Zipf's law corresponds to systems that are growing according to a maximally sustainable path in the…