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CHIARA FRANCESCHINI

Ricercatore Legge 240/10 - t.det.
Dipartimento di Scienze Fisiche, Informatiche e Matematiche sede ex-Matematica

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Pubblicazioni

2023 - A Joint Evaluation Methodology for Service Quality and User Privacy in Location Based Systems [Relazione in Atti di Convegno]
Bedogni, L.; Franceschini, C.; Montori, F.
abstract

Pervasive and ubiquitous applications provide novel and exciting services leveraging on a multitude of data obtained from people's devices, adapting the computation to the context in which the user currently is. This improves the service quality of these applications, which can provide a more tailored configuration of the application itself depending on the user context and needs. In these scenarios privacy is of paramount importance, since users must be also be protected against the misuse of their personal data. Analyzing ubiquitous systems in terms of service quality and privacy issues is however a challenging task, due to the heterogeneity of the possible attacks, which makes it difficult to compare two applications. In this paper we propose a novel methodology to jointly evaluate the service quality and the privacy issues in ubiquitous applications in an extensible and comparable way, building on the data available in each part of the system to be analyzed, and defining service qualities and privacy issues so that they can be easily re-used in other analyses. Our evaluation on a candidate application highlights the benefits of our proposal, showing the dependency between privacy levels and service quality, and paving the way for a novel methodology for the definition of these scenarios.

2023 - Hydrodynamical Behavior for the Symmetric Simple Partial Exclusion with Open Boundary [Articolo su rivista]
Franceschini, Chiara; Goncalves, Patricia; Salvador, Beatriz
abstract

2023 - Integrable heat conduction model [Articolo su rivista]
Franceschini, Chiara; Frassek, Rouven; Giardina, Cristian
abstract

We consider a stochastic process of heat conduction where energy is redistributed along a chain between nearest neighbor sites via an improper beta distribution. Similar to the well-known Kipnis-Marchioro-Presutti (KMP) model, the finite chain is coupled at its ends with two reservoirs that break the conservation of energy when working at different temperatures. At variance with KMP, the model considered here is integrable and one can write in a closed form the $n$-point correlation functions of the non-equilibrium steady state. As a consequence of the exact solution one can directly prove that the system is in a `local equilibrium' and described at the macro-scale by a product measure. Integrability manifests itself through the description of the model via the open Heisenberg chain with non-compact spins. The algebraic formulation of the model allows to interpret its duality relation with a purely absorbing particle system as a change of representation.

2022 - Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics [Articolo su rivista]
Franceschini, C.; Goncalves, P.; Sau, F.
abstract

We study the hydrodynamic and hydrostatic limits of the one-dimensional open symmetric inclusion process with slow boundary. Depending on the value of the parameter tuning the interaction rate of the bulk of the system with the boundary, we obtain a linear heat equation with either Dirichlet, Robin or Neumann boundary conditions as hydrodynamic equation. In our approach, we combine duality and first-second class particle techniques to reduce the scaling limit of the inclusion process to the limiting behavior of a single, non-interacting, particle.

2021 - Porous Medium Model: An Algebraic Perspective and the Fick’s Law [Relazione in Atti di Convegno]
De Paula, R.; Franceschini, C.
abstract

In this work, we study the porous medium model (PMM), an interacting particle system with nearest neighbor interactions of particles under some constraints. First, we consider the discrete space { 1, …, n- 1 } with additional Glauber dynamics acting respectively on sites 0 and n. We assume the hydrodynamic limit (proved in a companion paper [4]) and we prove that the Fick’s law holds. Moreover, we review how to construct a self-duality relation starting from the reversible measure of the process. Following this method, we show a self-duality result for the process without reservoirs, which is found inspired by its description via the Lie algebra su(2 ).

2021 - Q−orthogonal dualities for asymmetric particle systems [Articolo su rivista]
Carinci, G.; Franceschini, C.; Groenevelt, W.
abstract

We study a class of interacting particle systems with asymmetric interaction showing a self-duality property. The class includes the ASEP(q, θ), asymmetric exclusion process, with a repulsive interaction, allowing up to θ ∈ N particles in each site, and the ASIP(q, θ), θ ∈ R+, asymmetric inclusion process, that is its attractive counterpart. We extend to the asymmetric setting the investigation of orthogonal duality properties done in [8] for symmetric processes. The analysis leads to multivariate q−analogues of Krawtchouk polynomials and Meixner polynomials as orthogonal duality functions for the generalized asymmetric exclusion process and its asymmetric inclusion version, respectively. We also show how the q-Krawtchouk orthogonality relations can be used to compute exponential moments and correlations of ASEP(q, θ).

2019 - Orthogonal duality of Markov processes and unitary symmetries [Articolo su rivista]
Carinci, Gioia; Franceschini, Chiara; Giardina', Cristian; Groenevelt, WOLTER GODFRIED MATTIJS; Redig, Frank
abstract

We study self-duality for interacting particle systems, where the particles move as continuous time random walkers having either exclusion interaction or inclusion interaction. We show that orthogonal self-dualities arise from unitary symmetries of the Markov generator. For these symmetries we provide two equivalent expressions that are related by the Baker-Campbell-Hausdorff formula. The first expression is the exponential of an anti Hermitian operator and thus is unitary by inspection; the second expression is factorized into three terms and is proved to be unitary by using generating functions. The factorized form is also obtained by using an independent approach based on scalar products, which is a new method of independent interest that we introduce to derive (bi)orthogonal duality functions from non-orthogonal duality functions.

2019 - Stochastic Duality and Orthogonal Polynomials [Capitolo/Saggio]
Franceschini, C.; Giardina', C.
abstract

For a series of Markov processes we prove stochastic duality relations with duality functions given by orthogonal polynomials. This means that expectations with respect to the original process (which evolves the variable of the orthogonal polynomial) can be studied via expectations with respect to the dual process (which evolves the index of the polynomial). The set of processes include interacting particle systems, such as the exclusion process, the inclusion process and independent random walkers, as well as interacting diffusions and redistribution models of Kipnis–Marchioro–Presutti type. Duality functions are given in terms of classical orthogonal polynomials, both of discrete and continuous variable, and the measure in the orthogonality relation coincides with the process stationary measure.

2018 - Self-Duality of Markov Processes and Intertwining Functions [Articolo su rivista]
Franceschini, Chiara; Giardina', Cristian; Wolter, Groenevelt
abstract

We present a theorem which elucidates the connection between self-duality of Markov processes and representation theory of Lie algebras. In particular, we identify sufficient conditions such that the intertwining function between two representations of a certain Lie algebra is the self-duality function of a (Markov) operator. In concrete terms, the two representations are associated to two operators in interwining relation. The self-dual operator, which arise from an appropriate symmetric linear combination of them, is the generator of a Markov process. The theorem is applied to a series of examples, including Markov processes with a discrete state space (e.g. interacting particle systems) and Markov processes with continuous state space (e.g. diffusion processes). In the examples we use explicit representations of Lie algebras that are unitarily equivalent. As a consequence, in the discrete setting self-duality functions are given by orthogonal polynomials whereas in the continuous context they are Bessel functions.