Related papers: Compressibility and probabilistic proofs
We describe the relation between the isothermal atomic compressibility and density fluctuations in mixtures of two-component fermions with population or mass imbalance. We derive a generalized version of the fluctuation-dissipation theorem…
We extend the theoretical framework of proof mining by establishing general logical metatheorems that allow for the extraction of the computational content of theorems with prima facie "non-computational" proofs from probability theory,…
We address the question of convergence in the loopy belief propagation (LBP) algorithm. Specifically, we relate convergence of LBP to the existence of a weak limit for a sequence of Gibbs measures defined on the LBP s associated computation…
We discuss concrete examples for frame functions and their associated density operators, as well as for non-Gleason type probability measures.
We introduce a novel real-valued endogenous logic for expressing properties of probabilistic transition systems called Riesz modal logic. The design of the syntax and semantics of this logic is directly inspired by the theory of Riesz…
We study formal languages which are capable of fully expressing quantitative probabilistic reasoning and do-calculus reasoning for causal effects, from a computational complexity perspective. We focus on satisfiability problems whose…
Through a reformulation of the local limit theorem and law of small numbers, which is obtained by working in the spaces naturally associated to the limiting distributions, we discover a general and abstract framework for the investigation…
Recently, Brandt, Maus and Uitto [PODC'19] showed that, in a restricted setting, the dependency of the complexity of the distributed Lov\'asz Local Lemma (LLL) on the chosen LLL criterion exhibits a sharp threshold phenomenon: They proved…
This paper introduces a local optimization-based approach to test statistical hypotheses and to construct confidence intervals. This approach can be viewed as an extension of bootstrap, and yields asymptotically valid tests and confidence…
In this paper, we introduce a new defeasible version of propositional standpoint logic by integrating Kraus et al.'s defeasible conditionals, Britz and Varzinczak's notions of defeasible necessity and distinct possibility, along with…
Using the notion of existentially closed structures, we obtain embedding theorems for groups and Lie algebras. We also prove the existence of some groups and Lie algebras with prescribed properties.
In this short note, we shall prove some observations regarding the connection between indestructible $\omega_1$-guessing models and the $\omega_1$-approximation property of forcing notions.
We show how powerful algorithms recently developed for counting lattice points and computing volumes of convex polyhedra can be used to compute probabilities of a wide variety of events of interest in social choice theory. Several…
We establish an equivalent condition to the validity of the Collatz conjecture, using elementary methods. We derive some conclusions and show several examples of our results. We also offer a variety of exercises, problems and conjectures.
We give simple proofs, under minimal hypotheses, of the Weak Law of Large Numbers and the Central Limit Theorem for independent identically distributed random variables. These proofs use only the elementary calculus, together with the most…
We design hypersequent calculus proof systems for the theories of Riesz spaces and modal Riesz spaces and prove the key theorems: soundness, completeness and cut elimination. These are then used to obtain completely syntactic proofs of some…
In this work we prove the local multiplicity at most one theorem underlying the definition and theory of local $\gamma$-, $\epsilon$- and $L$-factors, defined by virtue of the generalized doubling method, over any local field of…
The idea of fully accepting statements when the evidence has rendered them probable enough faces a number of difficulties. We leave the interpretation of probability largely open, but attempt to suggest a contextual approach to full belief.…
I explain the difficulty of making various concepts of and relating to probability precise, rigorous and physically significant when attempting to apply them in reasoning about objects (e.g., spacetimes) living in infinite-dimensional…
We show the existence of regular combinatorial objects which previously were not known to exist. Specifically, for a wide range of the underlying parameters, we show the existence of non-trivial orthogonal arrays, t-designs, and t-wise…