arXiv subjects

Nicolò Paviato

Publications and source records attributed to Nicolò Paviato.

4 recordsLinked to original sources

arXiv2026

Central Limit Theorems for Finitary Factors of iid Processes

We study statistical limit theorems for time-series generated by multidimensional random fields that are finitary factors of iid random processes. Based on the decay of the tail of the coding radius, we establish the Central Limit Theorem with explicit rates of convergence, as well as the weak convergence to a Brownian sheet, for suitably regular functions. Our results can be applied to a variety of classical models in statistical mechanics, such as the Ising model, the hard-core model, and proper colourings.

math.PR↗

arXiv2026

Limiting behaviour of pattern counts in biased binary strings

For $p \in (0,1)$, sample a binary sequence from the infinite product measure of Bernoulli$(p)$ distributions. It is known that for $p=1/2$, almost every binary sequence is Poisson generic in the sense of Peres and Weiss, a property that reflects a specific statistical pattern in the frequency of finite substrings. However, this behaviour is highly exceptional: it fails for any $p \ne 1/2$. In these other cases, we show that the frequency of substrings of almost every sequence has either trivial or peculiar behaviour. Nevertheless, the Poisson limiting regime can be recovered if one restricts attention to substrings with a fixed number of successes in the Bernoulli$(p)$ trials.

math.PR↗

arXiv2026

Rates for maps and flows in a deterministic multidimensional weak invariance principle

We present the first rates of convergence to an $N$-dimensional Brownian motion when $N\ge2$ for discrete and continuous time dynamical systems. Additionally, we provide the first rates for continuous time in any dimension. Our results hold for nonuniformly hyperbolic and expanding systems, such as Axiom A flows, suspensions over a Young tower with exponential tails, and some classes of intermittent solenoids.

math.DS↗

arXiv2025

A threshold for Poisson behavior of non-stationary product measures

Let $γ_{n}= O (\log^{-c}n)$ and let $ν$ be the infinite product measure whose $n$-th marginal is Bernoulli$(1/2+γ_{n})$. We show that $c=1/2$ is the threshold, above which $ν$-almost every point is simply Poisson generic in the sense of Peres-Weiss, and below which this can fail. This provides a range in which $ν$ is singular with respect to the uniform product measure, but $ν$-almost every point is simply Poisson generic.

math.DS↗