Related papers: A walk with Goodstein
New numbers, called Guinness numbers, are introduced using certain function of natural argument. Few problems related to these numbers are formulated.
We investigate the overdamped stochastic dynamics of a particle in an asymptotically flat external potential field, in contact with a thermal bath. For an infinite system size, the particles may escape the force field and diffuse freely at…
We consider the limit behavior of a one-dimensional random walk with unit jumps whose transition probabilities are modified every time the walk hits zero. The invariance principle is proved in the scheme of series where the size of…
A new elementary proof of the prime number theorem presented recently in the framework of a scale invariant extension of the ordinary analysis is re-examined and clarified further. Both the formalism and proof are presented in a much more…
The ability to engineer non-Gaussian quantum resources underlies quantum technologies from communication and metrology to universal computation. However, while a number of canonical works have set no-go limits for attaining such resources…
The concentration of measure phenomenon may be summarized as follows: a function of many weakly dependent random variables that is not too sensitive to any of its individual arguments will tend to take values very close to its expectation.…
We study criteria for a ring - or more generally, for a small category - to be Gorenstein and for a module over it to be of finite projective dimension. The goal is to unify the universal coefficient theorems found in the literature and to…
We investigate fragments of generic absoluteness principles known as Maximality Principles. We determine the consistency strength of $\Sigma_n$-$\mathsf{MP}(\mathbb R)$ and $\Pi_n$-$\mathsf{MP}(\mathbb R)$, the boldface Maximality Principle…
This article is an attempt for a new vision of the basics of Physics, and of Relativity, in particular. A new generalized principle of inertia is proposed, as an universal principle, based on universality of the conservation laws, not…
Geoffrion's theorem is a fundamental result from mathematical programming assessing the quality of Lagrangian relaxation, a standard technique to get bounds for integer programs. An often implicit condition is that the set of feasible…
The Dirichlet forms methods, in order to represent errors and their propagation, are particularly powerful in infinite dimensional problems such as models involving stochastic analysis encountered in finance or physics, cf. [5]. Now, coming…
Galilean Relativity and Einstein's Special and General Relativity showed that the Laws of Physics go deeper than their representations in any given reference frame. Thus covariance, or independence of Laws of Physics with respect to changes…
The main objective of this paper is to develop extreme value theory for $\vartheta$-expansions. We establish the limit distribution of the maximum value in a $\vartheta$-continued fraction mixing stationary stochastic process, along with…
The newly discovered principle of maximum force makes it possible to summarize special relativity, quantum theory\se, and general relativity in one fundamental limit principle each. The three principles fully contain the three theories and…
We prove a structural result for measure preserving systems naturally associated with any finite collection of multiplicative functions that take values on the complex unit disc. We show that these systems have no irrational spectrum and…
We define a novel class of distances between statistical multivariate distributions by modeling an optimal transport problem on their marginals with respect to a ground distance defined on their conditionals. These new distances are metrics…
Zeckendorf's Theorem states that any positive integer can be uniquely decomposed into a sum of distinct, non-adjacent Fibonacci numbers. There are many generalizations, including results on existence of decompositions using only even…
In the base phi expansion any natural number is written uniquely as a sum of powers of the golden mean with coefficients 0 and 1, where it is required that the product of two consecutive digits is always 0. We tackle the problem of…
We derive a large deviation principle for families of random variables in the basin of attraction of spectrally positive stable distributions by proving a uniform version of the Tauberian theorem for Laplace-Stieltjes transforms. The main…
The splitting principle states that morphisms in a derived category do not "split" accidentally. This has been successsfully applied in several characterizations of rational, DB, and other singularities. In this article I prove a general…