arXiv subjects

Valerio Astuti

Publications and source records attributed to Valerio Astuti.

16 recordsLinked to original sources

arXiv2026

Italian Business-to-Business Invoicing Data: A Network Analysis

We present a comprehensive description of the network of Italian Business-to-Business commercial relationships, based on the universe of electronic invoices collected by the Italian Tax Office. The firm-to-firm detail of the data is exploited to describe the distribution of the numbers of buyers (customers) and sellers (suppliers) per firm, the centrality of each firm in the production network, and the average distance between firms. We characterize for the first time the firm-to-firm network describing the Italian production system, and present its geographic and sectoral breakdown. The analysis reveals heavy tailed distributions for the numbers of buyers and sellers per firm, implying a scale-free structure of the network. The distributions of centrality values display heavy tails as well, indicating a strong concentration of importance in a relatively small number of firms. We estimate the tail exponents for all these distributions, finding in all cases lower exponents for downstream (buyer-side) distributions than for the upstream (seller-side) ones.

cond-mat.stat-mech↗

arXiv2024

Who is in equilibrium?

In order to describe the properties of the observed distribution of wealth in a population, most economic models rely on the existence of an asymptotic equilibrium state. In addition, the process generating the equilibrium distribution is usually assumed to be ergodic, with a finite asymptotic average and bounded inequality. Here we show, using data from Bank of Italy's Survey on Household Income and Wealth and Forbes Italian billionaires lists, that the last hypothesis is not justified in Italy. We find that, even if an equilibrium asymptotic distribution exists, the average wealth has no finite asymptotic value. As a consequence we find that - without changes in the parameters of the wealth evolution process - wealth inequality is bound to diverge with time. In addition we evaluate the equilibration time of the evolution process when its parameters are chosen in order to admit both an equilibrium distribution and a finite equilibrium average wealth. Even when both the equilibrium hypotheses are satisfied, we find equilibration times much longer than the typical time span between economic shocks.

cond-mat.stat-mech↗

arXiv2023

A constraint on the dynamics of wealth concentration

In the context of a large class of stochastic processes used to describe the dynamics of wealth growth, we prove a set of inequalities establishing necessary and sufficient conditions in order to avoid infinite wealth concentration. These inequalities generalize results previously found only in the context of particular models, or with more restrictive sets of hypotheses. In particular, we emphasize the role of the additive component of growth - usually representing labor incomes - in limiting the growth of inequality. Our main result is a proof that in an economy with random wealth growth, with returns non-negatively correlated with wealth, an average labor income growing at least proportionally to the average wealth is necessary to avoid a runaway concentration. One of the main advantages of this result with respect to the standard economics literature is the independence from the concept of an equilibrium wealth distribution, which does not always exist in random growth models. We analyze in this light three toy models, widely studied in the economics and econophysics literature.

econ.TH↗

arXiv2022

A Bayesian algorithm for sample selection bias correction

In this paper we present a technique to couple non-traditional data with statistics based on survey data, in order to partially correct for the bias produced by non-random sample selections. All major social media platforms represent huge samples of the general population, generated by a self-selection process. This implies that they are not representative of the larger public, and there are problems in extrapolating conclusions drawn from these samples to the whole population. We present an algorithm to integrate these massive data with ones coming from traditional sources, with the properties of being less extensive but more reliable. This integration allows to exploit the best of both worlds and reach the detail of typical "big data" sources and the representativeness of a carefully designed sample survey.

stat.ME↗

arXiv2022

Efficient and accurate inference for mixtures of Mallows models with Spearman distance

The Mallows model occupies a central role in parametric modelling of ranking data to learn preferences of a population of judges. Despite the wide range of metrics for rankings that can be considered in the model specification, the choice is typically limited to the Kendall, Cayley or Hamming distances, due to the closed-form expression of the related model normalizing constant. This work instead focuses on the Mallows model with Spearman distance. An efficient and accurate EM algorithm for estimating finite mixtures of Mallows models with Spearman distance is developed, by relying on a twofold data augmentation strategy aimed at i) enlarging the applicability of Mallows models to samples drawn from heterogeneous populations; ii) dealing with partial rankings affected by diverse forms of censoring. Additionally, a novel approximation of the model normalizing constant is introduced to support the challenging model-based clustering of rankings with a large number of items. The inferential ability of the EM scheme and the effectiveness of the approximation are assessed by extensive simulation studies. Finally, we show that the application to three real-world datasets endorses our proposals also in the comparison with competing mixtures of ranking models.

stat.ME↗

arXiv2022

Theory and phenomenology of relativistic corrections to the Heisenberg principle

The Heisenberg position-momentum uncertainty principle shares with the equivalence principle the role of main pillar of our current description of nature. However, in its original formulation it is inconsistent with special relativity, and in nearly a century of investigation not much progress has been made toward a satisfactory reformulation. Some partial insight has been gained in the ultra-high-velocity regime but a full description is still missing and in particular we have no clue about the intermediate regime of particles whose speeds are much smaller than the speed of light but still high enough for tangible departures from the Heisenberg formulation to be present. As we stress here, that intermediate regime is also our best chance for testing experimentally our understanding of the implications of special relativity for the uncertainty principle. We here introduce a new approach to these challenges, based mainly on the observation that the only operative notion of position of a particle at a given time involves the crossing of the worldline of that particle with the worldline of a test particle. We find that the worldline-crossing perspective opens a path toward a special-relativistic version of the uncertainty principle, which indeed could be tested experimentally.

hep-th↗

arXiv2020

Multi-particle systems in quantum spacetime and a novel challenge for center-of-mass motion

In recent times there has been considerable interest in scenarios for quantum gravity in which particle kinematics is affected nonlinearly by the Planck scale, with encouraging results for the phenomenological prospects, but also some concerns that the nonlinearities might produce pathological properties for composite/multiparticle systems. We here focus on kinematics in the $κ$-Minkowski noncommutative spacetime, the quantum spacetime which has been most studied from this perspective, and compare the implications of the alternative descriptions of the total momentum of a multiparticle system which have been so far proposed. We provide evidence suggesting that priority should be given to defining the total momentum as the standard linear sum of the momenta of the particles composing the system. We also uncover a previously unnoticed feature concerning some (minute but conceptually important) effects on center-of-mass motion due to properties of the motion of the constituents relative to the center of mass.

gr-qc↗

arXiv2020

Effective Trap-like Activated Dynamics in a Continuous Landscape

We use a simple model to extend network models for activated dynamics to a continuous landscape with a well-defined notion of distance and a direct connection to many-body systems. The model consists of a tracer in a high-dimensional funnel landscape with no disorder. We find a non-equilibrium low-temperature phase with aging dynamics, that is effectively equivalent to that of models with built-in disorder, such as Trap Model, Step Model and REM.

cond-mat.dis-nn↗

arXiv2018

New analysis of the free energy cost of interfaces in spin glasses

In this work we want to enhance the calculation performed by Franz, Parisi and Virasoro (FPV) to estimate the free energy cost of interfaces in spin glasses and evaluate the lower critical dimension at which replica symmetry is restored. In particular we evaluate the free energy cost for a general class of effective Hamiltonians showing full replica symmetry breaking, and study the dependence of this cost on the order parameter and on the temperature. We confirm the findings of the FPV papers for the scaling of the free energy, recovering a value for the lower critical dimension of $D_{lc} = 2.5$. In addition to their results we find a non-trivial dependence of the free energy density cost on the order parameter and the temperature. Apart from the case of a restricted class of effective Hamiltonians this dependence cannot be expressed in terms of functions with a clear physical interpretation, as is the case in hierarchical models. In addition we connect the results on the lower critical dimension with recent simulations.

cond-mat.dis-nn↗

arXiv2018

Volume Entropy

Building on a technical result by Brunnemann and Rideout on the spectrum of the Volume operator in Loop Quantum Gravity, we show that the dimension of the space of the quadrivalent, diffeomorphism invariant states with no zero-volume nodes describing a region with total volume smaller than $V$, has \emph{finite} dimension, bounded by $V \log V$. This allows us to introduce the notion of "volume entropy" for this phase space: the von Neumann entropy associated to the measurement of volume.

gr-qc↗

arXiv2016

Statistical discrete geometry

Following our earlier work, we construct statistical discrete geometry by applying statistical mechanics to discrete (Regge) gravity. We propose a coarse-graining method for discrete geometry under the assumptions of atomism and background independence. To maintain these assumptions, restrictions are given to the theory by introducing cut-offs, both in ultraviolet and infrared regime. Having a well-defined statistical picture of discrete Regge geometry, we take the infinite degrees of freedom (large n) limit. We argue that the correct limit consistent with the restrictions and the background independence concept is not the continuum limit of statistical mechanics, but the thermodynamical limit.

gr-qc↗

arXiv2015

Lorentz invariant deformations of momentum space

In relative locality theories the geometric properties of phase space depart from the standard ones given by the fact that spaces of momenta are linear fibers over a spacetime base manifold. In particular here it is assumed that the momentum space is non linear and can therefore carry non trivial metric and composition law. We classify to second order all possible such deformations that preserve Lorentz invariance. We show that such deformations still exists after quotienting out by diffeomorphisms only if the non linear addition is non associative.

hep-th↗

arXiv2014

Misleading inferences from discretization of empty spacetime: Snyder-noncommutativity case study

Alternative approaches to the study of the quantum-gravity problem are handling the role of spacetime very differently. Some are focusing on the analysis of one or another novel formulation of "empty spacetime", postponing to later stages the introduction of particles and fields, while other approaches assume that spacetime should only be an emergent entity. We here argue that recent progress in the covariant formulation of quantum mechanics suggests that empty spacetime is not physically meaningful. We illustrate our general thesis in the specific context of the noncommutative Snyder spacetime, which is also of some intrinsic interest, since hundreds of studies were devoted to its analysis. We show that empty Snyder spacetime, described in terms of a suitable kinematical Hilbert space, is discrete, but this is only a formal artifact: the discreteness leaves no trace on the observable properties of particles on the physical Hilbert space.

hep-th↗

arXiv2013

Predictive description of Planck-scale-induced spacetime fuzziness

Several approaches to the quantum-gravity problem predict that spacetime should be "fuzzy", but have been so far unable to provide a crisp physical characterization of this notion. An intuitive picture of spacetime fuzziness has been proposed on the basis of semi-heuristic arguments, and in particular involves an irreducible Planck-scale contribution to the uncertainty of the energy of a particle. These arguments also inspired a rather active phenomenological programme looking for blurring of images of distant astrophysical sources that would result from such energy uncertainties. We here report the first ever physical characterization of spacetime fuzziness derived constructively within a quantum picture of spacetime, the one provided by spacetime noncommutativity. Our results confirm earlier heuristic arguments suggesting that spacetime fuzziness, while irrelevantly small on terrestrial scales, could be observably large for propagation of particles over cosmological distances. However, we find no Planck-scale-induced lower bound on the uncertainty of the energy of particles, and we observe that this changes how we should picture a quantum spacetime and also imposes a reanalysis of the associated phenomenology.

hep-th↗

arXiv2013

Gravity's weight on worldline fuzziness

We investigate a connection between recent results in 3D quantum gravity, providing an effective noncommutative-spacetime description, and some earlier heuristic descriptions of a quantum-gravity contribution to the fuzziness of the worldlines of particles. We show that 3D-gravity-inspired spacetime noncommutativity reflects some of the features suggested by previous heuristic arguments. Most notably, gravity-induced worldline fuzziness, while irrelevantly small on terrestrial scales, could be observably large for propagation of particles over cosmological distances.

gr-qc↗

arXiv2012

Relative locality in a quantum spacetime and the pregeometry of $κ$-Minkowski

We develop a new description of the much-studied $κ$-Minkowski noncommutative spacetime, centered on representing on a single Hilbert space not only the $κ$-Minkowski coordinates, but also the associated differential calculus and the $κ$-Poincaré symmetry generators. In this "pregeometric" representation the relevant operators act on the kinematical Hilbert space of the covariant formulation of quantum mechanics, which we argue is the natural framework for studying the implications of the step from commuting spacetime coordinates to the $κ$-Minkowski case, where the spatial coordinates do not commute with the time coordinate. The empowerment provided by this kinematical-Hilbert space representation allows us to give a crisp characterization of the "fuzziness" of $κ$-Minkowski spacetime, whose most striking aspect is a relativity of spacetime locality. We show that relative locality, which had been previously formulated exclusively in classical-spacetime setups, for a quantum spacetime takes the shape of a dependence of the fuzziness of a spacetime point on the distance at which an observer infers properties of the event that marks the point.

hep-th↗