Related papers: On measures driven by Markov chains
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…
We prove that if pure derivatives with respect to all coordinates of a function on $\mathbb{R}^n$ are signed measures, then their lower Hausdorff dimension is at least $n-1$. The derivatives with respect to different coordinates may be of…
The present paper studies a quantitative version of the transversality theorem. More precisely, given a continuous function $f\in \mathcal{C}([0,1]^d,\mathbb{R}^m)$ and a manifold $W\subset \mathbb{R}^m$ of dimension $p$, a sharpness result…
Let $f:X\to X$ be a dominating meromorphic map of a compact K\"ahler surface of large topological degree. Let $S$ be a positive closed current on $X$ of bidegree $(1,1)$. We consider an ergodic measure $\nu$ of large entropy supported by…
We discuss an extension to Voiculescu's formula for the quasicentral modulus of a tuple of commuting, self-adjoint operators with spectral measure absolutely continuous with respect to a generalized Hausdorff measure. These Hausdorff…
The main aim of this paper is to study the functional inequality \begin{equation*} \int_{[0,1]}f\bigl((1-t)x+ty\bigr)d\mu(t)\geq 0, \qquad x,y\in I \mbox{ with } x<y, \end{equation*} for a continuous unknown function $f:I\to{\mathbb R}$,…
We study the multifractal analysis of self-similar measures arising from random homogeneous iterated function systems. Under the assumption of the uniform strong separation condition, we see that this analysis parallels that of the…
Given a finite set $\mathcal{A} \subseteq \mathrm{SL}(2,\mathbb{R})$ we study the dimension of the attractor $K_\mathcal{A}$ of the iterated function system induced by the projective action of $\mathcal{A}$. In particular, we generalise a…
Infinite determinantal measures introduced in this note are inductive limits of determinantal measures on an exhausting family of subsets of the phase space. Alternatively, an infinite determinantal measure can be described as a product of…
The family $\mathcal{P}_{d}^{\lambda_{d-1}}$ of all probability measures on $[0,1]^d$ whose $(d-1)$-dimensional marginals are all equal to the Lebesgue measure $\lambda_{d-1}$ on $[0,1]^{d-1}$ contains remarkably pathological elements:…
We consider the problem of computing with many coins of unknown bias. We are given samples access to $n$ coins with \emph{unknown} biases $p_1,\dots, p_n$ and are asked to sample from a coin with bias $f(p_1, \dots, p_n)$ for a given…
Bernoulli convolutions form a one-parameter family of self-similar measures on the unit interval. We suggest to study their two-dimensional density which has an intricate combinatorial structure. Visualizing this structure we discuss…
We study certain multiple ergodic averages of an iterated functions system generated by two contractions on the unit interval. By using the dynamical coding ${0,1}^{\mathbb{N}}$ of the attractor, we compute the Hausdorff dimension of the…
Certain Bernoulli convolution measures (\mu) are known to be spectral. Recently, much work has concentrated on determining conditions under which orthonormal Fourier bases (i.e. spectral bases) exist. For a fixed measure known to be…
Under the formalism of annealed averaging of the partition function, a type of random multifractal measures with their multipliers satisfying exponentially distributed is investigated in detail. Branching emerges in the curve of generalized…
Let $\theta$ be a Bernoulli measure which is stationary for a random walk generated by finitely many contracting rational affine dilations of $\mathbb{R}^d$, and let $\mathcal{K} = \mathrm{supp}(\theta)$ be the corresponding attractor. An…
Multivariate orthogonal polynomials in $D$ real dimensions are considered from the perspective of the Cholesky factorization of a moment matrix. The approach allows for the construction of corresponding multivariate orthogonal polynomials,…
We introduce a Markov product structure for multivariate tail dependence functions, building upon the well-known Markov product for copulas. We investigate algebraic and monotonicity properties of this new product as well as its role in…
We estimate the energy and Hausdorff dimensions of the Riesz products on the unit sphere of $\mathbb{C}^n$, $n\ge 2$. Also, we obtain similar results for the pluriharmonic measures on the torus.
We deduce the existence of a maximal irreducibility measure for a Markov chain from Zorn's lemma.