Related papers: Amenability criterions and critical probabilities …
The well known bunkbed conjecture about percolation on finite graphs is now resolved; Gladkov, Pak and Zimin, building upon work of Hollom, have constructed a counterexample. We revisit this conjecture and study it in the broader context of…
The Giry monad on the category of measurable spaces sends a space to a space of all probability measures on it. There is also a finitely additive Giry monad in which probability measures are replaced by finitely additive probability…
In this note, we investigate Bernoulli oriented bond percolation with parameter $p$ on $\mathbb{Z}^2$. In addition to the standard edges, which are open with probability $p$, we introduce diagonal edges each open with probability…
We examine a new approach to modeling uncertainty based on plausibility measures, where a plausibility measure just associates with an event its plausibility, an element is some partially ordered set. This approach is easily seen to…
We describe a construction process of a relevant measure in any non-empty compact metric space. This probability measure has invariance properties with respect to isometric maps defined on open sets. These properties imply that this measure…
Entanglement is fundamental inasmuch because it rephrases the quest for the classical-quantum demarcation line, and it also has potentially enormous practical applications in modern information technology. In this work, employing the…
We show that probabilistic equivalence of a regret-based preference relationship over random variables is implied by a weak form of continuity and monotonicity.
We extend the jigsaw percolation model to analyze graphs where both underlying people and puzzle graphs are Erd\H{o}s-R\'enyi random graphs. Let $p_{\text{ppl}}$ and $p_{\text{puz}}$ denote the probability that an edge exists in the…
The projected discovery and exclusion capabilities of particle physics and astrophysics/cosmology experiments are often quantified using the median expected $p$-value or its corresponding significance. We argue that this criterion leads to…
The problem "A general characterization of uniqueness polynomial for non-critically injective polynomials" has been remained open since the last two decades. In this paper, we explore this open problem. To this end, we initiate a new…
We consider the directed percolation process as a prototype of systems displaying a nonequilibrium phase transition into an absorbing state. The model is in a critical state when the activation probability is adjusted at some precise value…
Entanglement, or quantum inseparability, is a crucial resource in quantum information applications, and therefore the experimental generation of separated yet entangled systems is of paramount importance. Experimental demonstrations of…
Although regular conditional distributions (r.c.d.) are well-defined and widely used measure-theoretic objects, they can violate our intuition from the classical definition of a conditional probability given an event. For that purpose, the…
The aim of this note is a proof of a recent conjecture of Kellner concerning the number of distinct prime factors of a particular product of primes. The proof uses profound results from analytic number theory, such as Granville-Ramar\'{e}'s…
Probabilistic team semantics is a framework for logical analysis of probabilistic dependencies. Our focus is on the axiomatizability, complexity, and expressivity of probabilistic inclusion logic and its extensions. We identify a natural…
In this paper, we take a fresh look at three Popperian concepts: riskiness, falsifiability, and truthlikeness (or verisimilitude) of scientific hypotheses or theories. First, we make explicit the dimensions that underlie the notion of…
We consider percolation on the Voronoi tessellation generated by a homogeneous Poisson point process on the hyperbolic plane. We show that the critical probability for the existence of an infinite cluster tends to $1/2$ as the intensity of…
Nadkarni's Theorem asserts that for a countable Borel equivalence relation (CBER) exactly one of the following holds: (1) It has an invariant Borel probability measure or (2) it admits a Borel compression, i.e., a Borel injection that maps…
Within classical propositional logic, assigning probabilities to formulas is shown to be equivalent to assigning probabilities to valuations. A novel notion of probabilistic entailment enjoying desirable properties of logical consequence is…
We introduce a method based on the finite size scaling assumption which allows to determine numerically the critical point and critical exponents related to observables in an infinite system starting from the knowledge of the observables in…