Related papers: Translation-invariant probability measures on enti…
We consider a randomly forced Ginzburg-Landau equation on an unbounded domain. The forcing is smooth and homogeneous in space and white noise in time. We prove existence and smoothness of solutions, existence of an invariant measure for the…
The equivalence of the characteristic function approach and the probabilistic approach to monotone and boolean convolutions is proven for non-compactly supported probability measures. A probabilistically motivated definition of the…
We develop a numerical approach for computing the additive, multiplicative and compressive convolution operations from free probability theory. We utilize the regularity properties of free convolution to identify (pairs of) `admissible'…
We extend the recent improvement of Roth's theorem on three term arithmetic progressions by Sanders to obtain similar results for the problem of locating non-trivial solutions to translation invariant linear equations in many variables in…
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…
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…
A space of entire functions of several complex variables rapidly decreasing on ${\mathbb R}^n$ and such that their growth along $i{\mathbb R}^n$ is majorized with the help of a family of weight functions is considered in this paper. For…
We introduced a new continued fraction expansions in our previous paper. For these expansions, we show formulae of probability about incomplete quotients. Furthermore, we prove the existence of invariant measures with respect to the…
In this thesis we study convolutions that arise from noncommutative probability theory. We prove several regularity results for free convolutions, and for measures in partially defined one-parameter free convolution semigroups. We discuss…
We show that there is only one Hilbert space of entire functions that is invariant under the action of naturally defined weighted translations.
We provide a sharp monotonicity theorem about the distribution of subharmonic functions on manifolds, which can be regarded as a new, measure theoretic form of the uncertainty principle. As an illustration of the scope of this result, we…
We prove that for certain partially hyperbolic skew-products, non-uniform hyperbolicity along the leaves implies existence of a finite number of ergodic absolutely continuous invariant probability measures which describe the asymptotics of…
We consider the nonparametric regression problem with multiple predictors and an additive error, where the regression function is assumed to be coordinatewise nondecreasing. We propose a Bayesian approach to make an inference on the…
We consider straight line flows on a translation surface that are minimal but not uniquely ergodic. We give bounds for the number of generic invariant probability measures.
We study the problem of estimating, in the sense of optimal transport metrics, a measure which is assumed supported on a manifold embedded in a Hilbert space. By establishing a precise connection between optimal transport metrics, optimal…
A compatible point-shift $F$ maps, in a translation invariant way, each point of a stationary point process $\Phi$ to some point of $\Phi$. It is fully determined by its associated point-map, $f$, which gives the image of the origin by $F$.…
It is well known that real measures on the circle are characterized by their Herglotz transform, an analytic function in the unit disc. Invariance of the measure under N-multiplication translates into a functional equation for the Herglotz…
We present a method for constructing global holomorphic peak functions from local holomorphic support functions for broad classes of unbounded domains. As an application, we establish a method for showing the positivity and completeness of…
Let $T$ be an ergodic measure-preserving transformation on a non-atomic probability space $(X,\Sigma,\mu)$. We prove uniform extensions of the Wiener-Wintner theorem in two settings: For averages involving weights coming from Hardy field…
We give an example of non-translation invariant product measure obtained from two translation invariant measures, one of which is non-sigma finite. This particular example also suggests that there can be infinitely many product measures if…