Related papers: Quantitative infinite mixing for non-compact skew …

We prove ergodicity of a class of infinite measure preserving systems, called skew-products. More precisely, we consider systems of the form \[ {T_f}:{[0, 1) \times \mathbb{R}}\to{[0, 1) \times \mathbb{R}},\quad {T_f(x, t)}:={(T(x),…

Let $G$ be a countable discrete sofic group. We define a concept of uniform mixing for measure-preserving $G$-actions and show that it implies completely positive sofic entropy. When $G$ contains an element of infinite order, we use this to…

We study skew-products of the form (x,\omega)\mapsto (Tx, \omega+\phi(x)) where T is a nonuniformly expanding map on a space X, preserving a (possibly singular) probability measure \tilde\mu, and \phi:X\to S^1 is a C^1 function. Under mild…

This work is devoted to the study of processes generated by random substitutions over a finite alphabet. We prove, under mild conditions on the substitution's rule, the existence of a unique process which remains invariant under the…

One of the goals of this article is to define a an unified setting adapted to the description of means (normalized integrals or invariant means) on an infinite product of measured spaces with infinite measure. We first remark that some…

As a natural counterpart to Nakada's $\alpha$-continued fraction maps, we study a one-parameter family of continued fraction transformations with an indifferent fixed point. We prove that matching holds for Lebesgue almost every parameter…

We consider the plus-phase of the two-dimensional Ising model below the critical temperature. In $1989$ Schonmann proved that the projection of this measure onto a one-dimensional line is not a Gibbs measure. After many years of continued…

In this work we obtain mixing (and in some cases sharp mixing rates) for a reasonable large class of invertible systems preserving an infinite measure. The examples considered here are the invertible analogue of both Markov and non Markov…

We find an extension of the quasi-metric (to be called $g$-quasi metric) such that the induced generalized topology may fail to form a topology. We show that $g$-quasi metrizability is a $g$-topologically invariant property of generalized…

We study fractality of unbounded sets of finite Lebesgue measure at infinity by introducing the notions of Minkowski dimension and content at infinity. We also introduce the Lapidus zeta function at infinity, study its properties and…

We consider Abelian covers of compact hyperbolic surfaces. We establish an asymptotic expansion of the correlations for the horocycle flow on $\mathbb{Z}^d$-covers, thus proving a strong form of Krickeberg mixing. We also prove that the…

We study compact hyperbolic surfaces and multiplication observables, establishing a large-scale analogue of Zelditch's quantum mixing theorem with hypotheses that hold for both arithmetic and Weil--Petersson random surfaces of large genus.…

This short review is devoted to measures on infinite dimensional spaces. We start by discussing product measures and projective techniques. Special attention is paid to measures on linear spaces, and in particular to Gaussian measures.…

Work in the measure algebra of the Lebesgue measure on the Cantor space: for comeager many $[A]$ the set of points $x$ such that the density of $x $ at $A$ is not defined is $\Sigma^{0}_{3}$-complete; for some compact $K$ the set of points…

Uniform integer-valued Lipschitz functions on a domain of size $N$ of the triangular lattice are shown to have variations of order $\sqrt{\log N}$. The level lines of such functions form a loop $O(2)$ model on the edges of the hexagonal…

We construct a function on the real line supported on a set of finite measure whose spectrum has density zero.

In this note, we discuss the derived functors of infinite products and homotopy limits. $QC(X)$, the category of quasi-coherent sheaves on a Deligne-Mumford stack $X$, usually has the property that the derived functors of product vanish…

We prove that the skew product over a linearly recurrent interval exchange transformation defined by almost any real-valued, mean-zero linear combination of characteristic functions of intervals is ergodic with respect to Lebesgue measure.

Motivated by de Finetti's representation theorem for almost exchangeable arrays, we want to sample $\mathbf p \in [0,1]^d$ from a distribution with density proportional to $\exp(-A^2\sum_{i<j}c_{ij}(p_i-p_j)^2)$, where $A$ is large and…

It is well-known that a strict analogue of the Birkhoff Ergodic Theorem in infinite ergodic theory is trivial; it states that for any infinite-measure-preserving ergodic system the Birkhoff average of every integrable function is almost…