L. Schiavo

activity

20162026

most citedThe Dirichlet-Ferguson Diffusion on the Space of Probability Measures over a Closed Riemannian Manifold

24 citations · 74 across the 23 of their papers we have counts for

collaborators

23 papers

math.DG2026

A 'global' Perspective on the Differential Geometry of Wasserstein Spaces

Lorenzo Dello Schiavo, Andrea Pinamonti

We develop a global differential calculus on the $L^{2}$ -Wasserstein space over a closed Riemannian manifold, based on derivations of cylinder functions rather than on the standard p…

math.FA2025

Non-linear Dirichlet Functionals: Markovianity, Locality, Invariance

Giovanni Brigati, Lorenzo Dello Schiavo

We present in a unified setting the foundations for a theory of non-linear Dirichlet functionals on Hilbert spaces. We prove known and new equivalences between non-linear semigroup…

math.FA2025

The Hellinger-Kantorovich metric measure geometry on spaces of measures

Lorenzo Dello Schiavo, Giacomo Enrico Sodini

Let $(M, g)$ be a Riemannian manifold with Riemannian distance $d_{g}$ , and $M (M)$ be the space of all non-negative Borel measures on $M$ , endowed with the Hellinge…

math.PR2025

Ill-posedness of the pure-noise Dean-Kawasaki equation

Lorenzo Dello Schiavo, Vitalii Konarovskyi

We prove that the Dean-Kawasaki-type stochastic partial differential equation $\partial ρ = \nabla \cdot (ρ ξ) + \nabla \cdot (ρ H (ρ))$ with vector-valued sp…

math.FA2024

Gradient flows of $(K, N)$ -convex functions with negative $N$

Lorenzo Dello Schiavo, Mattia Magnabosco, Chiara Rigoni

We discuss $(K, N)$ -convexity and gradient flows for $(K, N)$ -convex functionals on metric spaces, in the case of real $K$ and negative $N$ . In this generality, it is necessary to co…

math.PR2024★ 1 cited

Massive Particle Systems, Wasserstein Brownian Motions, and the Dean-Kawasaki Equation

Lorenzo Dello Schiavo

We develop a unifying theory for four different objects: (1) infinite systems of interacting massive particles; (2) solutions to the Dean-Kawasaki equation with singular drift and…

math.PR2023

Polychromatic Partitions, Kingman Theory, and Ewens Sampling Formula

Lorenzo Dello Schiavo, Filippo Quattrocchi

A polychromatic partition is a partition of a set of colored (marked) elements in which each block is recorded only by the number of elements of each color in that block. We introd…

math.MG2023

A Characterization of Maps of Bounded Compression

Lorenzo Dello Schiavo

A measurable map between measure spaces is shown to have bounded compression if and only if its image via the measure-algebra functor is Lipschitz-continuous w.r.t. the measure-alg…

math.OC2023

Local Conditions for Global Convergence of Gradient Flows and Proximal Point Sequences in Metric Spaces

Lorenzo Dello Schiavo, Jan Maas, Francesco Pedrotti

This paper deals with local criteria for the convergence to a global minimiser for gradient flow trajectories and their discretisations. To obtain quantitative estimates on the spe…

math.PR2023★ 2 cited

Wasserstein geometry and Ricci curvature bounds for Poisson spaces

Lorenzo Dello Schiavo, Ronan Herry, Kohei Suzuki

Let $Υ$ be the configuration space over a complete and separable metric base space, endowed with the Poisson measure $π$ . We study the geometry of $Υ$ from the…

math.PR2023★ 1 cited

Polyharmonic Fields and Liouville Quantum Gravity Measures on Tori of Arbitrary Dimension: from Discrete to Continuous

Lorenzo Dello Schiavo, Ronan Herry, Eva Kopfer +1

For an arbitrary dimension $n$ , we study: (a) the Polyharmonic Gaussian Field $h_{L}$ on the discrete torus $T_{L}^{n} = \frac{1}{L} Z^{n} / Z^{n}$ , that is th…

math.MG2022★ 2 cited

Configuration Spaces over Singular Spaces -- II. Curvature

Lorenzo Dello Schiavo, Kohei Suzuki

This is the second paper of a series on configuration spaces $Υ$ over singular spaces $X$ . Here, we focus on geometric aspects of the extended metric measure space $(Υ, \mathsf{d}_…

math.PR2021★ 3 cited

Scaling Limits of Random Walks, Harmonic Profiles, and Stationary Non-Equilibrium States in Lipschitz Domains

Lorenzo Dello Schiavo, Lorenzo Portinale, Federico Sau

We consider the open symmetric exclusion (SEP) and inclusion (SIP) processes on a bounded Lipschitz domain $Ω$ , with both fast and slow boundary. For the random walks on $Ω$ dual t…

math.GT2021

Effective contraction of skinning maps

Tommaso Cremaschi, Lorenzo Dello Schiavo

Using elementary hyperbolic geometry, we give an explicit formula for the contraction constant of the skinning map over moduli spaces of relatively acylindrical hyperbolic manifold…

math.PR2021★ 6 cited

Configuration spaces over singular spaces -- I. Dirichlet-Form and Metric Measure Geometry

Lorenzo Dello Schiavo, Kohei Suzuki

We construct a canonical differential structure on the configuration space $Υ$ over a singular base space $X$ and with a general invariant measure $μ$ on $Υ$ . We present an analyti…

math.FA2021★ 3 cited

Ergodic Decompositions of Dirichlet Forms under Order Isomorphisms

Lorenzo Dello Schiavo, Melchior Wirth

We study ergodic decompositions of Dirichlet spaces under intertwining via unitary order isomorphisms. We show that the ergodic decomposition of a quasi-regular Dirichlet space is…

math.PR2021

Conformally invariant random fields, quantum Liouville measures, and random Paneitz operators on Riemannian manifolds of even dimension

Lorenzo Dello Schiavo, Ronan Herry, Eva Kopfer +1

For large classes of even-dimensional Riemannian manifolds $(M, g)$ , we construct and analyze conformally invariant random fields. These centered Gaussian fields $h = h_{g}$ , called co-…

math.FA2020★ 11 cited

Rademacher-type Theorems and Sobolev-to-Lipschitz Properties for Strongly Local Dirichlet Spaces

Lorenzo Dello Schiavo, Kohei Suzuki

We extensively discuss the Rademacher and Sobolev-to-Lipschitz properties for generalized intrinsic distances on strongly local Dirichlet spaces possibly without square field opera…

math.PR2018★ 24 cited

The Dirichlet-Ferguson Diffusion on the Space of Probability Measures over a Closed Riemannian Manifold

L. Dello Schiavo

We construct a recurrent diffusion process with values in the space of probability measures over an arbitrary closed Riemannian manifold of dimension $d \geq 2$ . The process is assoc…

math.PR2018★ 6 cited

Characteristic Functionals of Dirichlet Measures

L. Dello Schiavo

We compute characteristic functionals of Dirichlet-Ferguson measures over a locally compact Polish space and prove continuous dependence of the random measure on the parameter meas…

math.FA2018★ 12 cited

A Rademacher-type Theorem on $L^{2}$ -Wasserstein Spaces over Closed Riemannian Manifolds

Lorenzo Dello Schiavo

Let $P$ be any Borel probability measure on the $L^{2}$ -Wasserstein space $(P_{2} (M), W_{2})$ over a closed Riemannian manifold $M$ . We consider the Dirichlet form $\mat…

math.PR2017★ 3 cited

A Mecke-type characterization of the Dirichlet-Ferguson measure

Lorenzo Dello Schiavo, Eugene W. Lytvynov

We prove a characterization of the Dirichlet-Ferguson measure over an arbitrary finite diffuse measure space. We provide an interpretation of this characterization in analogy with…

math.PR2016

Moments and Cumulants in Infinite Dimensions with Applications to Poisson, Gamma and Dirichlet-Ferguson Random Measures

L. Dello Schiavo

We show that the chaos representation of some Compound Poisson Type processes displays an underlying intrinsic combinatorial structure, partly independent of the chosen process. Fr…

A 'global' Perspective on the Differential Geometry of Wasserstein Spaces

Non-linear Dirichlet Functionals: Markovianity, Locality, Invariance

The Hellinger-Kantorovich metric measure geometry on spaces of measures

Ill-posedness of the pure-noise Dean-Kawasaki equation

Gradient flows of (K,N)-convex functions with negative N

Massive Particle Systems, Wasserstein Brownian Motions, and the Dean-Kawasaki Equation

Polychromatic Partitions, Kingman Theory, and Ewens Sampling Formula

A Characterization of Maps of Bounded Compression

Local Conditions for Global Convergence of Gradient Flows and Proximal Point Sequences in Metric Spaces

Wasserstein geometry and Ricci curvature bounds for Poisson spaces

Polyharmonic Fields and Liouville Quantum Gravity Measures on Tori of Arbitrary Dimension: from Discrete to Continuous

Configuration Spaces over Singular Spaces -- II. Curvature

Scaling Limits of Random Walks, Harmonic Profiles, and Stationary Non-Equilibrium States in Lipschitz Domains

Effective contraction of skinning maps

Configuration spaces over singular spaces -- I. Dirichlet-Form and Metric Measure Geometry

Ergodic Decompositions of Dirichlet Forms under Order Isomorphisms

Conformally invariant random fields, quantum Liouville measures, and random Paneitz operators on Riemannian manifolds of even dimension

Rademacher-type Theorems and Sobolev-to-Lipschitz Properties for Strongly Local Dirichlet Spaces

The Dirichlet-Ferguson Diffusion on the Space of Probability Measures over a Closed Riemannian Manifold

Characteristic Functionals of Dirichlet Measures

A Rademacher-type Theorem on L2-Wasserstein Spaces over Closed Riemannian Manifolds

A Mecke-type characterization of the Dirichlet-Ferguson measure

Moments and Cumulants in Infinite Dimensions with Applications to Poisson, Gamma and Dirichlet-Ferguson Random Measures

Gradient flows of $(K, N)$ -convex functions with negative $N$

A Rademacher-type Theorem on $L^{2}$ -Wasserstein Spaces over Closed Riemannian Manifolds