相关论文: Low for random reals and positive-measure dominati…
We show that degrees containing a complete extensions of arithmetic have the random join property: they are the supremum of any random real they compute, with another random real. The same is true for the truth-table and weak truth-table…
The aim of this paper is to present an elementary computable theory of random variables, based on the approach to probability via valuations. The theory is based on a type of lower-measurable sets, which are controlled limits of open sets,…
In this paper, we prove that for a topological dynamical system with positive mean topological dimension and marker property, it has factors of arbitrary small mean topological dimension and zero relative mean topological dimension which…
Topological measures and quasi-linear functionals generalize measures and linear functionals. We define and study deficient topological measures on locally compact spaces. A deficient topological measure on a locally compact space is a set…
We establish certain topological properties of rank understood as a function on the set of invariant measures on a topological dynamical system. To be exact, we show that rank is of Young class LU (i.e., it is the limit of an increasing…
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…
The notion of expansivity and its generalizations (measure expansive, measure positively expansive, continuum-wise expansive, countably-expansive) are well known for deterministic systems and can be a useful property for studying…
A class of rational functions characterized by some wonderful properties is studied. The properties that identify this class include simple algebra (their inverses can be expressed in radicals), simple topology (the total space of the…
We consider methods for obtaining local lower bounds on characteristics of quantum (correspondingly, classical) systems, i.e. lower bounds valid in the trace norm $\epsilon$-neighborhood of a given state (correspondingly, probability…
We consider transient nearest neighbor random walks on the positive part of the real line. We give criteria for the finiteness of the number of cutpoints and strong cutpoints. Examples and open problems are presented.
In this paper, we investigate properties of countable stationary towers. We derive the regularity properties of sets of reals in $L(\mathbf R)$ from some properties of countable stationary towers without explicit use of strong large…
Weak convergence of probability measures is one of the most important topics in the field probability and statistics. In this survey paper, we look at weak convergence of probability measures from the topological vector space point of view.…
The random measures on the space of continuous functions are considered. Stationary random measures are described. The weak solutions of the stochastic equations are substituted by the strong measure-valued solutions.
We reformulate slightly Russell's notion of typicality, so as to eliminate its circularity and make it applicable to elements of any first-order structure. We argue that the notion parallels Martin-L\"{o}f (ML) randomness, in the sense that…
In the first part of the paper we study orthogonality, domination, weight, regular and minimal types in the contexts of rosy and super-rosy theories. Then we try to develop analogous theory for arbitrary dependent theories.
We give a representation for regular forms associated with dominated $C_0$-semigroups which, in turn, characterises domination of $C_0$-semigroups associated with regular forms. In addition, we prove a relationship between the positivity of…
We construct random Morse functions on surfaces by random walk and compute related distributions. We study the space of Morse functions through these random variables. We consider subspaces characterized by the surfaces with boundary…
We use probabilistic methods to find lower bounds on the maximum number, in a graph with domination number \gamma, of dominating sets of size \gamma. We find that we can randomly generate a graph that, w.h.p., is dominated by almost all…
We investigate which infinite binary sequences (reals) are effectively random with respect to some continuous (i.e., non-atomic) probability measure. We prove that for every n, all but countably many reals are n-random for such a measure,…
In this paper we describe a theory of a cumulative distribution function on a space with an order from a probability measure defined in this space. This distribution function plays a similar role to that played in the classical case.…