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Giuseppe Tenaglia

Publications and source records attributed to Giuseppe Tenaglia.

7 recordsLinked to original sources
arXiv2026

Abundance of typical horseshoes for the random standard map

We introduce a notion of typical horseshoe, consisting of a pair of rectangles admitting Markov returns at times of positive lower density, with controlled hyperbolic geometry and orbits that shadow typical trajectories. We prove the abundance of typical horseshoes for the random standard map and establish several statistical properties of the system, including exponential mixing and large deviation estimates for the associated projective and two-point processes.

math.DS↗
arXiv2026

Stability of quasi-stationary measures in high-dimensional products of mixing Markov chains

We study high-dimensional conditioned dynamics obtained from an arbitrary number of independent copies of a mixing Markov chain. The dynamics is conditioned to avoid a family of holes whose stationary measure vanishes as the dimension grows, and we ask whether the resulting process admits a quasi-stationary measure close to the stationary product measure. Our problem is motivated by conditioning on holes with complicated geometry in high dimension, such as sets arising naturally from large deviations of suitable observables. Our main tool is the ANOVA decomposition, which separates functions according to their dependence on different subsets of coordinates. This allows us to exploit the product structure of the dynamics and obtain contraction estimates that are uniform in the dimension. Combined with a Keller Liverani perturbation argument, these estimates yield the existence of quasi-stationary densities converging to the stationary density as the size of the hole vanishes. Under stronger one-step mixing and regularization assumptions, we obtain sharper convergence in a Sobolev norm, with a square-root dependence on the measure of the hole. The improvement relies on the increasingly strong contraction of higher-order ANOVA components, thereby overcoming the usual loss of control with dimension. Finally, we apply our results to additive-noise Markov chains on the circle with smooth, uniformly positive transition densities

math.DS↗
arXiv2026

Uniform in time propagation of chaos for noisy mean-field coupled maps

We study discrete-time $N$-dimensional mean-field systems on the torus subject to additive noise whose probability density is bounded away from zero. Given a Lipschitz one-particle map and interaction term, we prove that, if the lower bound on the noise density is sufficiently large, the $N$-dimensional transfer operator $\mathcal P_N$ preserves a dimension-independent class of sub-Gaussian probability measures. Moreover, $\mathcal P_N$ is a one-step contraction in the Dobrushin-Wasserstein distance and therefore admits a unique invariant measure $ρ_N$, which is itself sub-Gaussian. Under the same condition on the noise strength, we show that the associated self-consistent transfer operator is a one-step contraction in Wasserstein distance and hence admits a unique fixed point $ρ$. We further prove, using these contraction estimates, that $\mathcal P_N$ preserves an $O(N^{-1/2})$ neighbourhood of the product measure $ρ^{\otimes N}$ in the Dobrushin-Wasserstein metric, and in particular that $ρ_N$ belongs to this neighbourhood. Finally, we establish uniform-in-time propagation of chaos in the Dobrushin-Wasserstein metric and, under the additional assumption that the noise density is of bounded variation, in total variation for every fixed-dimensional marginal.

math.DS↗
arXiv2025

Random Young towers and quenched decay of correlations for predominantly expanding multimodal circle maps

In this paper, we study the random dynamical system $f_ω^n$ generated by a family of maps $\{f_{ω_0}: \mathbb{S}^1 \to \mathbb{S}^1\}_{ω_0 \in [-\varepsilon,\varepsilon]},$ $f_{ω_0}(x) = αξ(x+ω_0) +a\ (\mathrm{mod }\ 1),$ where $ξ: \mathbb S^1 \to \mathbb R$ is a non-degenerated map, $a\in [0,1)$, and $α,\varepsilon>0$. Fixing a constant $c\in (0,1)$, we show that for $α$ sufficiently large and for $\varepsilon > α^{-1+c},$ the random dynamical system $f_ω^n$ presents a random Young tower structure and quenched decay of correlations.

math.DS↗
arXiv2024

Horseshoes for a class of nonuniformly expanding random dynamical systems on the circle

We propose a notion of random horseshoe for one-dimensional random dynamical systems. We prove the abundance of random horseshoes for a class of circle endomorphisms subject to additive noise, large enough to make the Lyapunov exponent positive. In particular, we provide conditions which guarantee that given any pair of disjoint intervals, for almost every noise realization, there exists a positive density sequence of return times to these intervals such that the induced dynamics are the full shift on two symbols.

math.DS↗