Related papers: Few more Comments on Benford's Law
We show that the frequency distribution of the first significant digits of the numbers in the data sets generated from a large class of measures of quantum correlations, which are either entanglement measures, or belong to the…
It is shown that the formula for the variance of combined series yields surprisingly simple proofs of some well known variance bounds.
We study the cycle structure of words in several random permutations. We assume that the permutations are independent and that their distribution is conjugation invariant, with a good control on their short cycles. If, after successive…
Benford's law is frequently used to evaluate the likihood that data is misrepresentative. Typically statistical tests measure the likihood. Another method of employing Benford's law is to compare the frequency of leading digits to the…
In this paper, we briefly discuss a mathematical concept that can be used in economics.
Up-down permutations are counted by tangent resp. secant numbers. Considering words instead, where the letters are produced by independent geometric distributions, there are several ways of introducing this concept; in the limit they all…
It is well-known that sequences such as the Fibonacci numbers and the factorials satisfy Benford's Law, that is, leading digits in these sequences occur with frequencies given by $P(d)=\log_{10}(1+1/d)$, $d=1,2,\dots,9$. In this paper, we…
It is argued from several points of view that quantum probabilities might play a role in statistical settings. New approaches toward quantum foundations have postulates that appear to be equally valid in macroscopic settings. One such…
We obtain an upper and lower bound for the number of reduced words for a permutation in terms of the number of braid classes and the number of commutation classes of the permutation. We classify the permutations that achieve each of these…
In this article, firstly, some simple and smoothness properties of the weighted numerical radius and the weighted Crawford number functions are investigated. Then, some generalization formulas for lower and upper bounds of the weighted…
We generalize the study of standard Lyndon loop words from [A.Negut, A.Tsymbaliuk, "Quantum loop groups and shuffle algebras via Lyndon words", Adv. Math. 439 (2024), Paper No. 109482] to a more general class of orders on the underlying…
This is a short commentary piece that discusses how the methods used in the natural sciences can apply to economics in general and financial markets specifically.
According to Zipf's meaning-frequency law, words that are more frequent tend to have more meanings. Here it is shown that a linear dependency between the frequency of a form and its number of meanings is found in a family of models of…
We prove a general ergodic-theoretic result concerning the return time statistic, which, properly understood, sheds some new light on the common sense phenomenon known as {\it the law of series}. Let \proc be an ergodic process on finitely…
The work takes another look at the number of runs that a string might contain and provides an alternative proof for the bound. We also propose another stronger conjecture that states that, for a fixed order on the alphabet, within every…
Three versions of the Weak Law of Large Numbers are proposed for weakly dependent and generally speaking non-equally distributed random variables, with finite or possibly infinite expectations.
Examples are given of q-deformed systems that may be interpreted by the standard rules of quantum theory in terms of new degrees of freedom and supplementary quantum numbers.
We present a proof of the Chevalley-Weil Theorem that is somewhat different from the proofs appearing in the literature and with somewhat weaker hypotheses, of purely topological type. We also provide a discussion of the assumptions, and an…
This short note provides a new and simple proof of the convergence rate for Peng's law of large numbers under sublinear expectations, which improves the corresponding results in Song [15] and Fang et al. [3].
This article presents the basis of a theory of entanglement. We begin with a classical theory of entangled discrete measures in Section~1. Section~2 treats quantum mechanics and discusses the statistics of bounded operators on a Hilbert…