相关论文: Measure free martingales

We prove general results about separation and weak$^\#$-convergence of boundedly finite measures on separable metric spaces and Souslin spaces. More precisely, we consider an algebra of bounded real-valued, or more generally a $*$-algebra…

Given a countable relational language $L$, we consider probability measures on the space of $L$-structures with underlying set $\mathbb{N}$ that are invariant under the logic action. We study the growth rate of the entropy function of such…

We introduce a probabilistic measure of naturalness (naturalness level) to fix naturalness bounds quantitatively. It is applied to the anomalous magnetic moments and the electric dipole moments due to new physics.

We develop analytic tools for studying the free multiplicative convolution of any measure on the real line and any measure on the nonnegative real line. More precisely, we construct the subordination functions and the $S$-transform of an…

For a metric measure space, we treat the set of distributions of 1-Lipschitz functions, which is called the 1-measurement. On the 1-measurement, we have a partial order relation by the Lipschitz order introduced by Gromov. The aim of this…

Preserving biodiversity and ecosystem stability is a challenge that can be pursued through modern statistical mechanics modeling. Here we introduce a variational maximum entropy-based algorithm to evaluate the entropy in a minimal ecosystem…

In the first part of this paper the notion of natural metric on the set of natural numbers is defined. It is such metric that the completion of N is a compact metric space that a probability borel measure exists in order that the sequence…

Uniform measures are defined as the functionals on the space of bounded uniformly continuous functions that are continuous on bounded uniformly equicontinuous sets. If every cardinal has measure zero then every countably additive measure is…

We show on theoretical grounds that, even in the presence of noise, probabilistic measurement strategies (which have a certain probability of failure or abstention) can provide, upon a heralded successful outcome, estimates with a precision…

We introduce on physical grounds a new measure of multipartite entanglement for pure states. The function we define is discriminant and monotone under LOCC and moreover can be expressed in terms of observables of the system.

In this paper, we derive power guarantees of some sequential tests for bounded mean under general alternatives. We focus on testing procedures using nonnegative supermartingales which are anytime valid and consider alternatives which…

Marginal structural models were introduced in order to provide estimates of causal effects from interventions based on observational studies in epidemiological research. The key point is that this can be understood in terms of Girsanov's…

We construct a function on the real line supported on a set of finite measure whose spectrum has density zero.

We give sufficient criteria for the Dol\'eans-Dade exponential of a stochastic integral with respect to a counting process local martingale to be a true martingale. The criteria are adapted particularly to the case of counting processes and…

In a recent paper, Melbourne and Terhesiu [Operator renewal theory and mixing rates for dynamical systems with infinite measure, Invent. Math. 189 (2012), 61-110] obtained results on mixing and mixing rates for a large class of…

Unpredictability, or randomness, of the outcomes of measurements made on an entangled state can be certified provided that the statistics violate a Bell inequality. In the standard Bell scenario where each party performs a single…

We propose a sequential, anytime-valid method to test the conditional independence of a response $Y$ and a predictor $X$ given a random vector $Z$. The proposed test is based on e-statistics and test martingales, which generalize likelihood…

We consider a deterministic system with two conserved quantities and infinity many invariant measures. However the systems possess a unique invariant measure when enough stochastic forcing and balancing dissipation are added. We then show…

On the space of unimodular lattices, we construct a sequence of invariant probability measures under a singular diagonal element with high entropy and show that the limit measure is 0.

In this paper we study a very general finite Ramsey theorem, where both the sets being colored and the homogeneous set must satisfy some largeness notion. For the homogeneous set this has already been done using the notion of…