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- Jean-René Chazottes, Sébastien Gouëzel
- 2011

For dynamical systems modeled by a Young tower with exponential tails, we prove an exponential concentration inequality for all separately Lipschitz observables of n variables. When tails are polynomial, we prove polynomial concentration inequalities. Those inequalities are optimal. We give some applications of such inequalities to specific systems and… (More)

We obtain moment and Gaussian bounds for general Lipschitz functions evaluated along the sample path of a Markov chain. We treat Markov chains on general (possibly unbounded) state spaces via a coupling method. If the first moment of the coupling time exists, then we obtain a variance inequality. If a moment of order 1+ ǫ of the coupling time exists, then… (More)

- Valentin S. Afraimovich, Jean-René Chazottes, Svetlana Katok
- 2000

Pointwise dimensions and spectra for measures associated with Poincaré recurrences are calculated for arbitrary weakly specified subshifts with positive entropy and for the corresponding special flows. It is proved that the Poincaré recurrence for a “typical” cylinder is asymptotically its length. Examples are provided which show that this is not true for… (More)

- Jean-René Chazottes, Jean-Marc Gambaudo, François Gautero, THURSTON SEMI-NORM, Jean-René Chazottes
- 2017

We show that the problem of tiling the Euclidean plane with a finite set of polygons (up to translation) boils down to prove the existence of zeros of a non-negative convex function defined on a finite-dimensional simplex. This function is a generalisation, in the framework of branched surfaces, of the Thurston semi-norm originally defined for compact… (More)

We present a new approach to estimate the relaxation speed to equilibrium of interacting particle systems. It is based on concentration inequalities and coupling. We illustrate our approach in a variety of examples for which we obtain several new results with short and non technical proofs. These examples include the symmetric and asymmetric exclusion… (More)

Let ∆ ( V be a proper subset of the vertices V of the defining graph of an irreducible and aperiodic shift of finite type (Σ+A, T ). Let ∆n be the union of cylinders in Σ + A corresponding to the points x for which the first n-symbols of x belong to ∆ and let μ be an equilibrium state of a Hölder potential φ on Σ+A. We know that μ(∆n) converges to zero as n… (More)

- Jean-René Chazottes, Renaud Leplaideur, Victor Le Gorgeu
- 2003

We study the time of nth return of orbits to some given (union of) rectangle(s) of a Markov partition of an Axiom A diffeomorphism. Namely, we prove the existence of a scaled generating function for these returns with respect to any Gibbs measure (associated to a Hölderian potential). As a by-product, we derive precise large deviation estimates and a… (More)

We introduce the multiplicative Ising model and prove basic properties of its thermodynamic formalism such as existence of pressure and entropies. We generalize to one-dimensional “layer-unique” Gibbs measures for which the same results can be obtained. For more general models associated to a d-dimensional multiplicative invariant potential, we prove a… (More)

We propose a geometric point of view to study the structure of ground states in lattice models, especially those with ‘non-periodic long-range order’ which can be seen as toy models for quasicrystals. In a lattice model, the configuration space is S d where S is a finite set, and Θ denotes action of the group Z by translation or ‘shift’. Given a… (More)

This letter echoes the article by T.C. Halsey and M.H. Jensen published in this journal [5]. To say it in a nutshell, the authors evoke various methods use to determine multifractal properties of strange attractors of dynamical systems, in particular from experimental data. They draw their attention on a method based on recurrence times used by S. Gratrix… (More)