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We consider biased random walks in positive random conductances on the d-dimensional lattice in the zero-speed regime and study their scaling limits. We obtain a functional Law of Large Numbers for the position of the walker, properly…
We obtain a lower bound for a number of primes in tuples. As applications, we obtain a lower bound for the Romanoff type representation functions.
In the setup of i.i.d.~observations and a real valued differentiable functional~$T$, locally asymptotic upper bounds are derived for the power of one-sided tests (simple, versus large values of~$T$)and for the confidence probability of…
A convenient measure of a map or flow's chaotic action is the topological entropy. In many cases, the entropy has a homological origin: it is forced by the topology of the space. For example, in simple toral maps, the topological entropy is…
A weak measurement consists in coupling a system to a probe in such a way that constructive interference generates a large output. So far, only the average output of the probe and its variance were studied. Here, the characteristic function…
A real $x$ is $\Delta^1_1$-Kurtz random ($\Pi^1_1$-Kurtz random) if it is in no closed null $\Delta^1_1$ set ($\Pi^1_1$ set). We show that there is a cone of $\Pi^1_1$-Kurtz random hyperdegrees. We characterize lowness for…
We show that under rather general circumstances, the almost everywhere pointwise inequality $|f|(x) \le Mf (x)$ is equivalent to a weak form of the Lebesgue density theorem, for totally bounded closed sets. We derive both positive and…
The subject of topological defects has become a very attractive field of study given its apparent relevance to as diverse systems as the early universe and condensed matter. As usually envisaged the topology of the manifold M of the minima…
In this paper we consider birational properties of ramification in excellent local rings. We give an example showing that local monomialization (and weak local monomialization) can fail for extensions of algebraic local rings in algebraic…
This is Part II of our work about random tensor inequalities and tail bounds for bivariate random tensor means. After reviewing basic facts about random tensors, we first consider tail bounds with more general connection functions. Then, a…
New features of systems with non-trivial topology such as fractional quantum numbers, inequivalent quantizations, good operators, topological anomalies, etc. are described in the framework of an algebraic quantization procedure on a group.…
In the present article, topological, metric, and fractal properties of certain sets are investigated. These sets are images of sets whose elements have restrictions on using digits or combinations of digits in own s-adic representations,…
For a measurable space ($X,\mathcal{A}$), let $\mathcal{M}(X,\mathcal{A})$ be the corresponding ring of all real valued measurable functions and let $\mu$ be a measure on ($X,\mathcal{A}$). In this paper, we generalize the so-called…
We examine the selective screenability property in topological groups. In the metrizable case we also give characterizations in terms of the Haver property and finitary Haver property respectively relative to left-invariant metrics. We…
We introduce a notion of vague convergence for random marked metric measure spaces. Our main result shows that convergence of the moments of order $k \ge 1$ of a random marked metric measure space is sufficient to obtain its vague…
For quantum field theories with topological sectors, Monte Carlo simulations on fine lattices tend to be obstructed by an extremely long auto-correlation time with respect to the topological charge. Then reliable numerical measurements are…
We show that with high probability the number of real zeroes of a random polynomial is bounded by the number of vertices on its Newton-Hadamard polygon times the cube of the logarithm of the polynomial degree. A similar estimate holds for…
From a research of several recent papers, in the first part, we are concerned with domination number in cubic graphs and give a sufficient condition of Reed's conjecture. In the second part, from a perspective, we study the structure of a…
We discuss the dependence of set-valued dynamical systems on parameters. Under mild assumptions which are often satisfied for random dynamical systems with bounded noise and control systems, we establish the fact that topological…
Tossing a coin is the most elementary Monte Carlo experiment. In a computer the coin is replaced by a pseudo random number generator. It can be shown analytically and by exact enumerations that popular random number generators are not…