Related papers: Ergodic lifts and overlap numbers

Heap monoids equipped with Bernoulli measures are a model of probabilistic asynchronous systems. We introduce in this framework the notion of asynchronous stopping time, which is analogous to the notion of stopping time for classical…

We consider matching with shifts for Gibbsian sequences. We prove that the maximal overlap behaves as $c\log n$, where $c$ is explicitly identified in terms of the thermodynamic quantities (pressure) of the underlying potential. Our…

Random Overlap Structures (ROSt's) are random elements on the space of probability measures on the unit ball of a Hilbert space, where two measures are identified if they differ by an isometry. In spin glasses, they arise as natural limits…

We construct an equivariant microlocal lift for locally symmetric spaces. In other words, we demonstrate how to lift, in a ``semi-canonical'' fashion, limits of eigenfunction measures on locally symmetric spaces to Cartan-invariant measures…

In this paper we develop a new approach for studying overlapping iterated function systems. This approach is inspired by a famous result due to Khintchine from Diophantine approximation. This result shows that for a family of limsup sets,…

The robust statistical description of dynamical systems under perturbations is a central problem in ergodic theory. In this paper, we investigate the statistical properties of skew-product maps driven by a subshift of finite type with…

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),…

We consider the limit set of generalised iterated function systems. Under the assumption of a natural potential, the so called cylinder function, we prove the existence of the invariant probability measure satisfying the equilibrium state.…

We consider a generic class of log-concave, possibly random, (Gibbs) measures. We prove the concentration of an infinite family of order parameters called multioverlaps. Because they completely parametrise the quenched Gibbs measure of the…

We study the ergodic properties (recurrence, discrepancy, diffusion coefficients and ergodicity itself) of a class of $\mathbb Z$-extensions over infinite interval exchange transformations called rotated odometers. The choice of a…

In this paper we show that in systems where the probability distribution of the the overlap is non trivial in the infinity volume limit, the property of ultrametricity can be proved in general starting from two very simple and natural…

The nature of equilibrium states in disordered materials is often studied using an overlap function P(q), the probability of two configurations having similarity q. Exact sampling simulations of a two-dimensional proxy for three-dimensional…

We study the optimization of ergodic averages for multi-valued dynamical systems, i.e. where points may have multiple different forward orbits. Under upper semi-continuity assumptions, we show that the maximum space average with respect to…

We consider a special case of the question of classification of invariant Radon measures of $\mathbb{Z}^m$-valued skew-products over interval exchange transformations, which arise as Poincar\'e sections of the linear flow on periodic…

We prove ergodicity in a class of skew-product extensions of interval exchange transformations given by cocycles with logarithmic singularities. This, in particular, gives explicit examples of ergodic $\mathbb{R}$-extensions of minimal…

We study the sample-to-sample fluctuations of the overlap probability densities from large-scale equilibrium simulations of the three-dimensional Edwards-Anderson spin glass below the critical temperature. Ultrametricity, Stochastic…

In [11], employing the technique of noncommutative interpolation, a maximal ergodic theorem in noncommutative Lp-spaces, 1 < p < infinity, was established and, among other things, corresponding maximal ergodic inequalities and individual…

Under the assumption of a natural subadditive potential, the so called cylinder function, working on the symbol space we prove the existence of the ergodic invariant probability measure satisfying the equilibrium state. As an application we…

We show that for odd-valued piecewise-constant skew products over a certain two parameter family of interval exchanges, the skew product is ergodic for a full-measure choice of parameters.

For a dynamical system satisfying the approximate product property and asymptotically entropy expansiveness, we characterize a delicate structrue of the space of invariant measures: The ergodic measures of intermediate entropies and…