Related papers: Benford's Law and Continuous Dependent Random Vari…
According to a popular belief, the decimal digits of mathematical constants such as {\pi} behave like statistically independent random variables, each taking the values 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 with equal probability of 1/10. If…
Thanks to the increasing availability in computing power, high-dimensional engineering problems seem to be at reach. But the curse of dimensionality will always prevent us to try out extensively all the hypotheses. There is a vast…
We establish a strong law of large numbers for one-dimensional continuous-time random walks in dynamic random environments under two main assumptions: the environment is required to satisfy a decoupling inequality that can be interpreted as…
We consider a model of randomness for self-similar Cantor sets of finite and positive $1$-Hausdorff measure. We find the sharp rate of decay of the probability that a Buffon needle lands $\delta$-close to a Cantor set of this particular…
We give a construction of a real number that is normal to all integer bases and continued fraction normal. The computation of the first n digits of its continued fraction expansion performs in the order of n^4 mathematical operations. The…
For scientific computations on a digital computer the set of real number is usually approximated by a finite set F of "floating-point" numbers. We compare the numerical accuracy possible with difference choices of F having approximately the…
Long birth time series for Romania are investigated from Benford's law point of view, distinguishing between families with a religious (Orthodox and Non-Orthodox) affiliation. The data extend from Jan. 01, 1905 till Dec. 31, 2001, i.e. over…
Conformity with Benford's Law is widely used to detect irregularities in numerical datasets, particularly in accounting, finance, and economics. However, the statistical tools commonly used for this purpose (such as Chi-squared, MAD, or KS)…
We explore a possibility of measuring deviation from the exponential decay law in pure quantum systems. The power law behavior at late times of decay time profile is predicted in quantum mechanics, and has been experimentally attempted to…
We show that the laws of Zipf and Benford, obeyed by scores of numerical data generated by many and diverse kinds of natural phenomena and human activity are related to the focal expression of a generalized thermodynamic structure. This…
DNA data storage systems encode digital data into DNA strands, enabling dense and durable storage. Efficient data retrieval depends on coverage depth, a key performance metric. We study the random access coverage depth problem and focus on…
Some properties of diagonal binomial coefficients were studied in respect to frequency of their units digits. An approach was formulated that led to use of difference tables to predict if certain units digits can appear in the values of…
We show that for most choices of an initial seed $x_0$, the sequence of the first $N$ iterates of $x_0$ under the $3x+1$ map approximately satisfies Benford's law.
In a prime number decomposition of integers in a given set, the occurrence frequencies of prime numbers are shown to satisfy a general forms of Zipf's law.
In the probability theory limit distributions (or probability measures) are often characterized by some convolution equations (factorization properties) rather than by Fourier transforms (the characteristic functionals). In fact, usually…
A necessary and sufficient condition ("nonresonance") is established for every solution of an autonomous linear difference equation, or more generally for every sequence $(x^\top A^n y)$ with $x,y\in \mathbb{R}^d$ and $A\in…
Consider a coin tossing experiment which consists of tossing one of two coins at a time, according to a renewal process. The first coin is fair and the second has probability $1/2 + \theta$, $\theta \in [-1/2,1/2]$, $\theta$ unknown but…
We say that a convergence law holds for a sequence of random combinatorial objects if, for any first-order sentence $\varphi$, the proportion of objects satisfying $\varphi$ converges to a limiting value as the size of the objects tends to…
Let $f(z)=\sum_{n=1}^\infty \lambda_f(n)e^{2\pi i n z}\in S_{k}^{new}(\Gamma_0(N))$ be a normalized Hecke eigenform of even weight $k\geq2$ on $\Gamma_0(N)$ without complex multiplication. Let $\mathbb{P}$ denote the set of all primes. We…
We consider a system composed of a fixed number of particles with total energy smaller or equal to some prescribed value. The particles are non-interacting, indistinguishable and distributed over fixed number of energy levels. The energy…