Related papers: Infinite Determinantal Measures
In \cite{Ch91a} it was shown that the billiard ball map for the periodic Lorentz gas has infinite topological entropy. In this article we study the set of points with infinite Lyapunov exponents. Using the cell structure developed in…
We derive analytic expressions for infinite products of random 2x2 matrices. The determinant of the target matrix is log-normally distributed, whereas the remainder is a surprisingly complicated function of a parameter characterizing the…
We consider suitable weak solutions of 2-dimensional Euler equations on bounded domains, and show that the class of completely random measures is infinitesimally invariant for the dynamics. Space regularity of samples of these random fields…
A causal set is a countably infinite poset in which every element is above finitely many others; causal sets are exactly the posets that have a linear extension with the order-type of the natural numbers -- we call such a linear extension a…
We study deviation of ergodic averages for dynamical systems given by self-similar tilings on the plane and in higher dimensions. The main object of our paper is a special family of finitely-additive measures for our systems. An asymptotic…
Building on recent results regarding symmetric probabilistic constructions of countable structures, we provide a method for constructing probability measures, concentrated on certain classes of countably infinite structures, that are…
In the article a new measure in infinite dimensional unite cube different from the Haar or product measures is constructed. Some differences between introduced measure and the product measure are discussed.
This note gives an explicit description of conditional measures for the determinantal point process with the Bergman kernel.
A determinantal point process (DPP) is an ensemble of random nonnegative-integer-valued Radon measures, whose correlation functions are all given by determinants specified by an integral kernel called the correlation kernel. First we show…
Localization and dilation procedures are discussed for infinite dimensional $\alpha$-concave measures on abstract locally convex spaces (following Borell's hierarchy of hyperbolic measures).
We define an infinite measure-preserving transformation to have infinite symmetric ergodic index if all finite Cartesian products of the transformation and its inverse are ergodic, and show that infinite symmetric ergodic index does not…
We establish sharp global rigidity upper bounds for universal determinantal point processes describing edge eigenvalues of random matrices. For this, we first obtain a general result which can be applied to general (not necessarily…
We study a measure-theoretic notion of connectedness for sets of finite perimeter in the setting of doubling metric measure spaces supporting a weak $(1,1)$-Poincar\'{e} inequality. The two main results we obtain are a decomposition theorem…
We prove the existence of a successful coupling for $n$ particles in the symmetric inclusion process. As a consequence we characterize the ergodic measures with finite moments, and obtain sufficient conditions for a measure to converge in…
Determinantal process is a dynamical extension of a determinantal point process such that any spatio-temporal correlation function is given by a determinant specified by a single continuous function called the correlation kernel.…
For a broad class of point processes, including determinantal point processes, we construct associated marked and conditional ensembles, which allow to study a random configuration in the point process, based on information about a randomly…
There is studied an invariant measure structure of a class of ergodicl discrete dynamical systems by means of the measure generating function method
Entanglement in nonequilibrium systems is considered. A general definition for entanglement measure is introduced, which can be applied for characterizing the level of entanglement produced by arbitrary operators. Applying this definition…
We define a large class of multifractal random measures and processes with arbitrary log-infinitely divisible exact or asymptotic scaling law. These processes generalize within a unified framework both the recently defined log-normal…
We consider the action of Mandelbrot multiplicative cascades on probability measures supported on a symbolic space. For general probability measures, we obtain almost a sharp criterion of non-degeneracy of the limiting measure; it relies on…