Related papers: Subcomputable Schnorr Randomness
As computability implies value definiteness, certain sequences of quantum outcomes cannot be computable.
We consider some random series parametrised by complex binary strings. The simplest case is that of Rademacher series, independent of a time parameter. This is then extended to the case of Fourier series on the circle with Rademacher…
We propose the construction of entire functions with a given random collection of zeros. There are considered two particular cases. In the first one we are dealing with simple zeros. And the second corresponds to random zeros with random…
Statisticians often use Monte Carlo methods to approximate probability distributions, primarily with Markov chain Monte Carlo and importance sampling. Sequential Monte Carlo samplers are a class of algorithms that combine both techniques to…
A set C of reals is said to be negligible if there is no probabilistic algorithm which generates a member of C with positive probability. Various classes have been proven to be negligible, for example the Turing upper-cone of a…
We study the question, ``For which reals $x$ does there exist a measure $\mu$ such that $x$ is random relative to $\mu$?'' We show that for every nonrecursive $x$, there is a measure which makes $x$ random without concentrating on $x$. We…
A new number system, the set of the non-Dedekindian numbers, is introduced and characterized axiomatically. It is then proved that any hypercontinous hyperreal number system is strictly included in the set of the Non-Dedekindian Numbers.…
Random sets are used to get a continuous partition of the cardinality of the union of many overlapping sets. The formalism uses M\"obius transforms and adapts Shapley's methodology in cooperative game theory, into the context of set theory.…
The problem of covariance estimation for replicated surface-valued processes is examined from the functional data analysis perspective. Considerations of statistical and computational efficiency often compel the use of separability of the…
We present a way of introducing joint distibution function and its marginal distribution functions for non-compatible observables. Each such marginal distribution function has the property of commutativity. Models based on this approach can…
Probabilistic submeasures generalizing the classical (numerical) submeasures are introduced and discussed in connection with some classes of aggregation functions. A special attention is paid to triangular norm-based probabilistic…
Many automatic sequences, such as the Thue-Morse sequence or the Rudin-Shapiro sequence, have some desirable features of pseudorandomness such as a large linear complexity and a small well-distribution measure. However, they also have some…
We study algorithmic randomness notions via effective versions of almost-everywhere theorems from analysis and ergodic theory. The effectivization is in terms of objects described by a computably enumerable set, such as lower semicomputable…
Motivated by the subordinated Brownian motion, we define a new class of (in general discontinuous) random fields on higher-dimensional parameter domains: the subordinated Gaussian random field. We investigate the pointwise marginal…
By the sometimes so-called 'Main Theorem' of Recursive Analysis, every computable real function is necessarily continuous. We wonder whether and which kinds of HYPERcomputation allow for the effective evaluation of also discontinuous…
This paper proposes an alternative language for expressing results of the algorithmic theory of randomness. The language is more precise in that it does not involve unspecified additive or multiplicative constants, making mathematical…
We provide a self-contained introduction to random matrices. While some applications are mentioned, our main emphasis is on three different approaches to random matrix models: the Coulomb gas method and its interpretation in terms of…
As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a stochastic maximal inequality derived by using It\^o's formula and on a new…
As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a {\em stochastic maximal inequality} derived by using the formula for…
Quantifying uncertainty in predictions or, more generally, estimating the posterior conditional distribution, is a core challenge in machine learning and statistics. We introduce Convex Nonparanormal Regression (CNR), a conditional…