arXiv subjects

S. Gallo

Publications and source records attributed to S. Gallo.

8 recordsLinked to original sources

arXiv2026

Finitary coding and Gaussian concentration for random fields

We study Gaussian concentration inequalities for random fields obtained as finitary codings of i.i.d.\ fields, linking concentration properties to coding structure. A finitary coding represents a dependent field as a shift-equivariant image of an i.i.d.\ process, where each output depends on a finite but configuration-dependent portion of the input. Gaussian concentration corresponds to uniform sub-Gaussian bounds for local observables. Our main abstract result shows that Gaussian concentration is preserved under finitary codings with finite second moment of the coding volume. The proof relies on a refinement of the bounded-differences inequality, due to Talagrand and Marton, handling configuration-dependent influences. Under an additional structural assumption, satisfied in particular by coupling-from-the-past codings, a finite first moment suffices. These moment conditions are sharp. We apply these results to Gibbs measures, Markov random fields on $\mathbb Z^d$, and a broad class of one-dimensional processes. Using recent constructions of finitary codings, notably by Spinka and collaborators, we obtain sharp necessary and sufficient conditions for Gaussian concentration in classical lattice models, including the Ising, Potts, and random-cluster models: it holds if and only if the model lies in the full uniqueness regime, extending previous results beyond strict subregimes. In one dimension, we treat processes with possibly unbounded memory. For countable-state Markov chains, we obtain equivalent characterizations in terms of geometric ergodicity, exponential return-time tails, and finitary i.i.d.\ codings with exponential tails.

math.PR↗

arXiv2025

Pathwise guessing in categorical time series with unbounded alphabets

The following learning problem arises naturally in various applications: Given a finite sample from a categorical or count time series, can we learn a function of the sample that (nearly) maximizes the probability of correctly guessing the values of a given portion of the data using the values from the remaining parts? Unlike classical approaches in statistical inference, our approach avoids explicitly estimating the conditional probabilities. We propose a non-parametric guessing function with a learning rate independent of the alphabet size. Our analysis focuses on a broad class of time series models that encompasses finite-order Markov chains, some hidden Markov chains, Poisson regression for count processes, and one-dimensional Gibbs measures. We provide a margin condition that controls the rate of convergence for the risk. Additionally, we establish a minimax lower bound for the convergence rate of the risk associated with our guessing problem. This lower bound matches the upper bound achieved by our estimator up to a logarithmic factor, demonstrating its near-optimality.

math.ST↗

arXiv2022

Gas distribution from clusters to filaments in IllustrisTNG

Matter distribution in the environment of galaxy clusters, from their cores to their connected cosmic filaments, must be in principle related to the underlying cluster physics and it evolutionary state. We aim to investigate how radial and azimuthal distribution of gas is affected by cluster environments, and how it can be related to cluster mass assembly history. Radial physical properties of gas (velocity, temperature, and density) is first analysed around 415 galaxy cluster environments from IllustrisTNG simulation at z = 0 (TNG300-1). Whereas hot plasma is virialised inside clusters (< R200), the dynamics of warm hot inter-galactic medium (WHIM) can be separated in two regimes: accumulating and slowly infalling gas at cluster peripheries and fast infalling motions outside clusters (> 1.5R200). The azimuthal distribution of dark matter (DM), hot and warm gas phases is secondly statistically probed by decomposing their 2-D distribution in harmonic space. Inside clusters, the azimuthal symmetries of DM and hot gas are well tracing cluster structural properties, such as their center offsets, substructure fractions and elliptical shapes. Beyond cluster virialised regions, we find that WHIM gas follows the azimuthal distribution of DM thus tracing cosmic filament patterns. Azimuthal symmetries of hot and warm gas distribution are finally shown to be imprints of cluster mass assembly history, strongly correlated with the formation time, mass accretion rate, and dynamical state of clusters. Azimuthal mode decomposition of 2-D gas distribution is a promising probe to assess the 3-D physical and dynamical cluster properties up to their connected cosmic filaments.

astro-ph.CO↗

arXiv2020

Self-Switching Markov Chains: emerging dominance phenomena

In many dynamical systems in nature, the law of the dynamics changes along with the temporal evolution of the system. These changes are often associated with the occurrence of certain events. The timing of occurrence of these events depends, in turn, on the trajectory of the dynamical system itself, making the dynamics of the system and the timing of a change in the dynamics strongly coupled. Naturally, trajectories that take longer to satisfy the event will last longer. Therefore, we expect to observe more frequently the dominant dynamics, the ones that take longer to change in the long run. This article proposes a Markov chain model, called Self-Switching Markov Chain (SSMC), in which the emergence of dominant dynamics can be rigorously addressed. We present conditions and scaling in the SSMC under which we observe with probability one only the subset of dominant dynamics, and we characterize these dominant dynamics. Furthermore, we show that the switching between dynamics exhibits metastability-like property.

math.PR↗

arXiv2020

Optimal Gaussian concentration bounds for stochastic chains of unbounded memory

We obtain optimal Gaussian concentration bounds (GCBs) for stochastic chains of unbounded memory (SCUMs) on countable alphabets. These stochastic processes are also known as "chains with complete connections" or "$g$-measures". We consider two different conditions on the kernel: (1) when the sum of its oscillations is less than one, or (2) when the sum of its variations is finite, i.e., belongs to $\ell^1(\mathbb{N})$. We also obtain explicit constants as functions of the parameters of the model. The proof is based on maximal coupling. Our conditions are optimal in the sense that we exhibit examples of SCUMs that do not have GCB and for which the sum of oscillations is strictly larger than one, or the variation belongs to $\ell^{1+ε}(\mathbb{N})$ for any $ε> 0$. These examples are based on the existence of phase transitions. We also extend the validity of GCB to a class of functions which can depend on infinitely many coordinates. We illustrate our results by three applications. First, we derive a Dvoretzky-Kiefer-Wolfowitz type inequality which gives a uniform control on the fluctuations of the empirical measure. Second, in the finite-alphabet case, we obtain an upper bound on the $\bar{d}$-distance between two stationary SCUMs and, as a by-product, we obtain new (explicit) bounds on the speed of Markovian approximation in $\bar{d}$. Third, we obtain exponential rate of convergence for Birkhoff sums of a certain class of observables.

math.PR↗

arXiv2019

Galactic axions search with a superconducting resonant cavity

To account for the dark matter content in our Universe, post-inflationary scenarios predict for the QCD axion a mass in the range $(10-10^3)\,μ\mbox{eV}$. Searches with haloscope experiments in this mass range require the monitoring of resonant cavity modes with frequency above 5\,GHz, where several experimental limitations occur due to linear amplifiers, small volumes, and low quality factors of Cu resonant cavities. In this paper we deal with the last issue, presenting the result of a search for galactic axions using a haloscope based on a $36\,\mbox{cm}^3$ NbTi superconducting cavity. The cavity worked at $T=4\,\mbox{K}$ in a 2\,T magnetic field and exhibited a quality factor $Q_0= 4.5\times10^5$ for the TM010 mode at 9\,GHz. With such values of $Q$ the axion signal is significantly increased with respect to copper cavity haloscopes. Operating this setup we set the limit $g_{aγγ}<1.03\times10^{-12}\,\mbox{GeV}^{-1}$ on the axion photon coupling for a mass of about 37\,$μ$eV. A comprehensive study of the NbTi cavity at different magnetic fields, temperatures, and frequencies is also presented.

physics.ins-det↗

arXiv2019

The complete $L^q$-spectrum and large deviations for return times for equilibrium states with summable potentials

Let $(X_k)_{k\geq 0}$ be a stationary and ergodic process with joint distribution $\mu$ where the random variables $X_k$ take values in a finite set $\mathcal{A}$. Let $R_n$ be the first time this process repeats its first $n$ symbols of output. It is well-known that $\frac{1}{n}\log R_n$ converges almost surely to the entropy of the process. Refined properties of $R_n$ (large deviations, multifractality, etc) are encoded in the return-time $L^q$-spectrum defined as \[ \mathcal{R}(q)=\lim_n\frac{1}{n}\log\int R_n^q \,d\mu\quad (q\in\mathbb{R}) \] provided the limit exists. We consider the case where $(X_k)_{k\geq 0}$ is distributed according to the equilibrium state of a potential $\varphi:\mathcal{A}^{\mathbb{N}}\to\mathbb{R}$ with summable variation, and we prove that \[ \mathcal{R}(q) = \begin{cases} P((1-q)\varphi) & \text{for}\;\; q\geq q_\varphi^*\\ \sup_\eta \int \varphi \, d\eta & \text{for}\;\; q<q_\varphi^{*} \end{cases} \] where $P((1-q)\varphi)$ is the topological pressure of $(1-q)\varphi$, the supremum is taken over all shift-invariant measures, and $q_\varphi^*$ is the unique solution of $P((1-q)\varphi) =\sup_\eta \int \varphi \, d\eta$. Unexpectedly, this spectrum does not coincide with the $L^q$-spectrum of $\mu_\varphi$, which is $P((1-q)\varphi)$, and does not coincide with the waiting-time $L^q$-spectrum in general. In fact, the return-time $L^q$-spectrum coincides with the waiting-time $L^q$-spectrum if and only if the equilibrium state of $\varphi$ is the measure of maximal entropy. As a by-product, we also improve the large deviation asymptotics of $\frac{1}{n}\log R_n$.

math.DS↗

arXiv2018

Searching for galactic axions through magnetized media: QUAX status report

The current status of the QUAX R\&D program is presented. QUAX is a feasibility study for a detection of axion as dark matter based on the coupling to the electrons. The relevant signal is a magnetization change of a magnetic material placed inside a resonant microwave cavity and polarized with a static magnetic field.

physics.ins-det↗