相关论文: Multiplicative monotone convolutions

Let X be a smooth projective Berkovich space over a complete discrete valuation field K of residue characteristic zero, endowed with an ample line bundle L. We introduce a general notion of (possibly singular) semipositive (or…

We construct a new random probability measure on the sphere and on the unit interval which in both cases has a Gibbs structure with the relative entropy functional as Hamiltonian. It satisfies a quasi-invariance formula with respect to the…

Evaluating joint probabilities of potential outcomes and observed variables, and their linear combinations, is a fundamental challenge in causal inference. This paper addresses the bounding and identification of these probabilities in…

We establish new conditions for obtaining uniform bounds on the moments of discrete-time stochastic processes. Our results require a weak negative drift criterion along with a state-dependent restriction on the sizes of the one-step jumps…

As physics searches for invariants in observations, this paper looks for invariants of probabilistic observation without assuming physical structure. Structure emerges from the basic assumption of science that new information shall lead to…

Let $\mu$ and $\nu$ be two probability measures on $\R^d$, where $\mu(\d x)= \e^{-V(x)}\d x$ for some $V\in C^1(\R^d)$. Explicit sufficient conditions on $V$ and $\nu$ are presented such that $\mu*\nu$ satisfies the log-Sobolev, Poincar\'e…

In this paper we introduce a biparametric family of transformations which can be seen as an extension of the so-called up and down transformations. This new class of transformations allows to us to introduce new informational functionals,…

We study the discrete-time evolution of a transformation on a set of probability measures that is up-dated combining independently the marginals on the atoms of partitions. This model was recently introduced in Baake, Baake and Salamat…

Let $s(n)$ denote the number of ones in the binary expansion of a natural number $n\in\mathbb{N}$. For any $t\in\mathbb{N}$ and $d\in\mathbb{Z}$, let $\mu_t(d)$ denote the asymptotic density of the set of those natural numbers $n$ for which…

The Gauss-Minkowski correspondence in $\mathbb{R}^2$ states the existence of a homeomorphism between the probability measures $\mu$ on $[0,2\pi]$ such that $\int_0^{2\pi} e^{ix}d\mu(x)=0$ and the compact convex sets (CCS) of the plane with…

We show from a categorical point of view that probability measures on certain measurable or topological spaces arise canonically as the extension of probability distributions on countable sets. We do this by constructing probability monads…

It is shown that the free multiplicative convolution of two nondegenerate probability measures on the unit circle has no continuous singular part relative to arclength measure. Analogous results have long been known for free additive…

This paper is motivated by relations between association and independence of random variables. It is well-known that for real random variables independence implies association in the sense of Esary, Proschan and Walkup, while for random…

Multiplicative invariance is a well-studied property of subsets of the unit interval. The theory in the complex plane is less developed. This paper introduces an analogous definition for multiplicative invariance in the complex plane…

It is well known that the space of invariant probability measures for transitive sub-shifts of finite type is a Poulsen simplex. In this article we prove that in the non-compact setting, for a large family of transitive countable Markov…

For a class of piecewise deterministic Markov processes, the supports of the invariant measures are characterized. This is based on the analysis of controllability properties of an associated deterministic control system. Its invariant…

We present new examples of superintegrable matrix/eigenvalue models. These examples arise as a result of the exploration of the relationship between the theory of superintegrability and multivariate orthogonal polynomials. The new…

Using a characterization of Mutual Complete Dependence copulas, we show that, with respect to the Sobolev norm, the MCD copulas can be approximated arbitrarily closed by shuffles of Min. This result is then used to obtain a characterization…

Selberg and Morris integral probability distributions are long conjectured to be distributions of the total mass of the Bacry-Muzy Gaussian Multiplicative Chaos measures with non-random logarithmic potentials on the unit interval and…

Let mu be a probability measure on the unit circle and nu be the measure formed by adding a pure point to mu. We give a formula for the Verblunsky coefficients of the perturbed measure, based on a result of Simon.