Related papers: Measure rigidity for algebraic bipermutative cellu…

Let S be a nonexceptional oriented surface of finite type. We construct an uncountable family of probability measures on the space of area on holomorphic quadratic differentials over the moduli space for S containing the usual Lebesgue…

A conjecture of Ulam states that the standard probability measure $\pi$ on the Hilbert cube $I^\omega$ is invariant under the induced metric $d_a$ when the sequence $a = \{ a_i \}$ of positive numbers satisfies the condition…

Let $G$ be a real Lie group, $\Lambda<G$ a lattice and $H<G$ a connected semisimple subgroup without compact factors and with finite center. We define the notion of $H$-expanding measures $\mu$ on $H$ and, applying recent work of…

The asymptotic behavior of a cellular automaton iterated on a random configuration is well described by its limit probability measure(s). In this paper, we characterize measures and sets of measures that can be reached as limit points after…

A finitely-additive measure $\lambda $ on an infinite-dimensional real Hilbert space $E$ which is invariant with respect to shifts and orthogonal mappings has been defined. This measure can be considered as the analog of the Lebesgue…

Suppose $\{f_1,...,f_m\}$ is a set of Lipschitz maps of $\mathbb{R}^d$. We form the iterated function system (IFS) by independently choosing the maps so that the map $f_i$ is chosen with probability $p_i$ ($\sum_{i=1}^m p_i=1$). We assume…

We construct a family of probability measures on the group of Hamiltonian diffeomorphisms of a closed symplectic manifold $(M,\omega)$. We show that these measures are Borel measures with respect to the topology induced by the Hofer metric.…

The fiducial coincides with the posterior in a group model equipped with the right Haar prior. This result is here generalized. For this the underlying probability space of Kolmogorov is replaced by a $\sigma$-finite measure space and…

Using results relating the complexity of a two dimensional subshift to its periodicity, we obtain an application to the well-known conjecture of Furstenberg on a Borel probability measure on $[0,1)$ which is invariant under both $x\mapsto…

Every word $w$ in the free group $F_r$ of rank $r$ induces a probability measure (the $w$-measure) on every compact group $G$, by substitution of Haar-random $G$-elements in the letters. This measure is determined by its Fourier…

We consider a minimal equicontinuous action of a finitely generated group $G$ on a Cantor set $X$ with invariant probability measure $\mu$, and stabilizers of points for such an action. We give sufficient conditions under which there exists…

We consider $(M,d)$ a connected and compact manifold and we denote by $X$ the Bernoulli space $M^{\mathbb{N}}$. The shift acting on $X$ is denoted by $\sigma$. We analyze the general XY model, as presented in a recent paper by A. T.…

Let $\alpha: G\curvearrowright X$ be a minimal free continuous action of an infinite countable amenable group on an infinite compact metrizable space. In this paper, under the hypothesis that the invariant ergodic probability Borel measure…

Motivated by recent investigations of Sophie Grivaux and \'Etienne Matheron on the existence of invariant measures in Linear Dynamics, we introduce the concept of locally bounded orbit for a continuous linear operator $T:X\longrightarrow X$…

An (asynchronous) automaton transformation of one-sided infinite words over p-letter alphabet Fp = Z/pZ, where p is a prime, is a continuous transformation (w.r.t. the p-adic metric) of the ring of p-adic integers Zp. Moreover, an automaton…

Certain fermionic quantum field theories are equivalent to probabilistic cellular automata, with fermionic occupation numbers associated to bits. We construct an automaton that represents a discrete model of spinor gravity in four…

In this paper, we prove (global) $q$-Poincar\'e inequalities for probability measures on nilpotent Lie groups with filiform Lie algebra of any length. The probability measures under consideration have a density with respect to the Haar…

We consider the locally thinned Bernoulli field on $\mathbb Z^d$, which is the lattice version of the Type-I Mat\'ern hardcore process in Euclidean space. It is given as the lattice field of occupation variables, obtained as image of an…

We study a model of spatial random permutations over a discrete set of points. Formally, a permutation $\sigma$ is sampled proportionally to the weight $\exp\{-\alpha \sum_x V(\sigma(x)-x)\},$ where $\alpha>0$ is the temperature and $V$ is…

A Borel probability measure \( \mu \) with compact support on \( \mathbb{R}^n \) is called spectral measure if there exists a discrete set \( \Lambda \subset \mathbb{R}^n \) such that \( E_\Lambda := \{e^{2\pi i \langle \lambda, x \rangle}:…