Related papers: Note on $f_\lambda$-statistical convergence

We review some aspects of moduli in string theory. We argue that one should focus on {\it approximate moduli spaces}, and that there is evidence that such spaces exist non-perturbatively. We ask what it would mean for string theory to…

Contemporary statistical publications rely on simulation to evaluate performance of new methods and compare them with established methods. In the context of meta-analysis of log-odds-ratios, we investigate how the ways in which simulations…

We introduce a novel framework for uncertainty quantification in clustering that combines martingale posterior distributions with density-based clustering. Unlike classical model-based approaches, which define clusters at the latent level…

In this article, we establish the mod-$\phi$ convergence of the major index of a uniform random standard tableau whose shape converges in the Thoma simplex. This implies various probabilistic estimates, in particular speed of convergence…

We survey old and new results on the existence of moduli spaces of semistable coherent sheaves both in algebraic and in complex geometry.

This is a review article on mirror symmetry and aspects of it related to the theory of modular forms. We describe this topic along its historical development and connect to some more recent results toward the end. The article is for…

We introduce the notion of density of a rational language with respect to a sequence of probability measures. We prove that if $(\mu_n)$ is a sequence of Bernoulli measures converging to a positive Bernoulli measure $\overline{\mu}$, the…

We introduce a multiscale test statistic based on local order statistics and spacings that provides simultaneous confidence statements for the existence and location of local increases and decreases of a density or a failure rate. The…

For a given prime $p$, we determine the limit, as $\lambda \to \infty$, of the density of residues modulo $p^\lambda$ attained by the Fibonacci sequence. In particular, we show that this limiting density is related to zeros in the sequence…

We study vertex algebras and their modules associated with possibly degenerate even lattices, using an approach somewhat different from others. Several known results are recovered and a number of new results are obtained. We also study…

The Collatz Conjecture's connection to dynamical systems opens it to a variety of techniques aimed at recurrence and density results. First, we turn to density results and strengthen the result of Terras through finding a strict rate of…

In this article we study the expanding properties of random perturbations of contracting Lorenz maps satisfying the summability condition of exponent 1. Under general conditions on the maps and perturbation types, we prove stochastic…

In this note, convergence of random variables will be revisited. We will give the answers to 5 questions among the 6 open questions introduced in (Convergence rates in the law of large numbers and new kinds of convergence of random…

We formulate conditions for convergence of Laws of Large Numbers and show its links with of the parts of mathematical analysis such as summation theory, convergence of orthogonal series. We present also applications of the Law of Large…

This paper is concerned with the study of the fractional finite sums theory. We present the classes of functions for which it is possible to characterize the constant related to the derivative of fractional sums (denominated by essence of a…

Statistical limits are defined relaxing conditions on conventional convergence. The main idea of the statistical convergence of a sequence l is that the majority of elements from l converge and we do not care what is going on with other…

Based on the concept of new type of statistical convergence defined by Aktuglu, we have introduced the weighted $\alpha\beta$ - statistical convergence of order $\theta$ in case of fuzzy functions and classified it into pointwise, uniform…

To provide a solid analytic foundation for the module approach to conditional risk measures, our purpose is to establish a complete random convex analysis over random locally convex modules by simultaneously considering the two kinds of…

Several results in functional analysis are extended to the setting of $L^0$-modules, where $L^0$ denotes the ring of all measurable functions $x\colon \Omega\to \mathbb{R}$. The focus is on results involving compactness. To this end, a…

We study the Lp-integrated risk of some classical estimators of the density, when the observations are drawn from a strictly stationary sequence. The results apply to a large class of sequences, which can be non-mixing in the sense of…