Vittoria Silvestri
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Vittoria Silvestri has a total of 8 co-authors. Here are the top co-authors by number of shared publications:
- Lionel Levine
Cornell University
5 shared publications - Alessandra Faggionato
Department of Mathematics, Sapienza University of Rome, Roma, Italy
4 shared publications - Amanda Turner
University of Leeds
3 shared publications - James R. Norris
Statistical Laboratory, University of Cambridge, Centre for Mathematical Sciences, Cambridge, UK
3 shared publications - Nathanaël Berestycki
University of Vienna Austria
2 shared publications Alessandra Faggionato
1 shared publication
Latest Publications
- Open Access
Internal Diffusion Limited Aggregation with Critical Branching Random Walks
Internal Diffusion Limited Aggregation is an interacting particle system that describes the growth of a random cluster governed by the boundary harmonic measure seen from an internal point. Our paper studies IDLA in $\mathbb{Z}^d$ driven by critical branching random walks. We prove that, unlike classical IDLA, this process exhibits a phase transition in the dimension. More precisely, we establish the existence of a spherical shape theorem in dimension $d\geq 3$ and the absence of a spherical shape theorem for $d \leq 2$. Our bounds on the inner and outer worst deviations are of polynomial nature, which we expect to be a feature of this model.Open AccessInternal Diffusion Limited Aggregation with Critical Branching Random Walks
Internal Diffusion Limited Aggregation is an interacting particle system that describes the growth of a random cluster governed by the boundary harmonic measure seen from an internal point. Our paper studies IDLA in $\mathbb{Z}^d$ driven by critical branching random walks. We prove that, unlike classical IDLA, this process exhibits a phase transition in the dimension. More precisely, we establish the existence of a spherical shape theorem in dimension $d\geq 3$ and the absence of a spherical shape theorem for $d \leq 2$. Our bounds on the inner and outer worst deviations are of polynomial nature, which we expect to be a feature of this model. - Open Access
- 6 March 2024
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 405 (3) , 1-78
Stability of Regularized Hastings–Levitov Aggregation in the Subcritical Regime
We prove bulk scaling limits and fluctuation scaling limits for a two-parameter class ALE $$({\alpha },\eta )$$ of continuum planar aggregation models. The class includes regularized versions of the Hastings–Levitov family HL $$({\alpha })$$ and continuum versions of the family of dielectric-breakdown models, where the local attachment intensity for new particles is specified as a negative power $$-\eta $$ of the density of arc length with respect to harmonic measure. The limit dynamics follow solutions of a certain Loewner–Kufarev equation, where the driving measure is made to depend on the solution and on the parameter $${\zeta }={\alpha }+\eta $$ . Our results are subject to a subcriticality condition $${\zeta }\leqslant 1$$ : this includes HL $$({\alpha })$$ for $${\alpha }\leqslant 1$$ and also the case $${\alpha }=2,\eta =-1$$ corresponding to a continuum Eden model. Hastings and Levitov predicted a change in behaviour for HL $$({\alpha })$$ at $${\alpha }=1$$ , consistent with our results. In the regularized regime considered, the fluctuations around the scaling limit are shown to be Gaussian, with independent Ornstein–Uhlenbeck processes driving each Fourier mode, which are seen to be stable if and only if $${\zeta }\leqslant 1$$ .- 6 March 2024
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 405 (3) , 1-78
Open AccessStability of Regularized Hastings–Levitov Aggregation in the Subcritical Regime
We prove bulk scaling limits and fluctuation scaling limits for a two-parameter class ALE $$({\alpha },\eta )$$ of continuum planar aggregation models. The class includes regularized versions of the Hastings–Levitov family HL $$({\alpha })$$ and continuum versions of the family of dielectric-breakdown models, where the local attachment intensity for new particles is specified as a negative power $$-\eta $$ of the density of arc length with respect to harmonic measure. The limit dynamics follow solutions of a certain Loewner–Kufarev equation, where the driving measure is made to depend on the solution and on the parameter $${\zeta }={\alpha }+\eta $$ . Our results are subject to a subcriticality condition $${\zeta }\leqslant 1$$ : this includes HL $$({\alpha })$$ for $${\alpha }\leqslant 1$$ and also the case $${\alpha }=2,\eta =-1$$ corresponding to a continuum Eden model. Hastings and Levitov predicted a change in behaviour for HL $$({\alpha })$$ at $${\alpha }=1$$ , consistent with our results. In the regularized regime considered, the fluctuations around the scaling limit are shown to be Gaussian, with independent Ornstein–Uhlenbeck processes driving each Fourier mode, which are seen to be stable if and only if $${\zeta }\leqslant 1$$ . - 1 January 2024
- Published by Institute for Applied and Pure Mathematics (IMPA) in Latin American Journal of Probability and Mathematical Statistics
- Vol. 21 (2) , 863-906
A martingale approach to time-dependent and time-periodic linear response in Markov jump processes
- 1 January 2024
- Published by Institute for Applied and Pure Mathematics (IMPA) in Latin American Journal of Probability and Mathematical Statistics
- Vol. 21 (2) , 863-906
A martingale approach to time-dependent and time-periodic linear response in Markov jump processes
- Open Access
Universality Conjectures for Activated Random Walk
Activated Random Walk is a particle system displaying Self-Organized Criticality, in that the dynamics spontaneously drive the system to a critical state. How universal is this critical state? We state many interlocking conjectures aimed at different aspects of this question: scaling limits, microscopic limits, temporal and spatial mixing, incompressibility, and hyperuniformity.
Open AccessUniversality Conjectures for Activated Random Walk
Activated Random Walk is a particle system displaying Self-Organized Criticality, in that the dynamics spontaneously drive the system to a critical state. How universal is this critical state? We state many interlocking conjectures aimed at different aspects of this question: scaling limits, microscopic limits, temporal and spatial mixing, incompressibility, and hyperuniformity.
- Open Access
- 1 January 2023
- Published by International Press of Boston in Arkiv för Matematik
- Vol. 61 (1) , 41-66
Explosive growth for a constrained Hastings-Levitov aggregation model
We consider a constrained version of the HL(0) Hastings-Levitov model of aggregation in the complex plane, in which particles can only attach to the part of the cluster that has already been grown. Although one might expect that this gives rise to a non-trivial limiting shape, we prove that the cluster grows explosively: in the upper half plane, the aggregate accumulates infinite diameter as soon as it reaches positive capacity. More precisely, we show that after nt particles of (half-plane) capacity 1/(2n) have attached, the diameter of the shape is highly concentrated around root t log n, uniformly in t is an element of[0, T]. This illustrates a new instability phenomenon for the growth of single trees/fjords in unconstrained HL(0).
- 1 January 2023
- Published by International Press of Boston in Arkiv för Matematik
- Vol. 61 (1) , 41-66
Open AccessExplosive growth for a constrained Hastings-Levitov aggregation model
We consider a constrained version of the HL(0) Hastings-Levitov model of aggregation in the complex plane, in which particles can only attach to the part of the cluster that has already been grown. Although one might expect that this gives rise to a non-trivial limiting shape, we prove that the cluster grows explosively: in the upper half plane, the aggregate accumulates infinite diameter as soon as it reaches positive capacity. More precisely, we show that after nt particles of (half-plane) capacity 1/(2n) have attached, the diameter of the shape is highly concentrated around root t log n, uniformly in t is an element of[0, T]. This illustrates a new instability phenomenon for the growth of single trees/fjords in unconstrained HL(0).
- Open Access
Explosive growth for a constrained Hastings-Levitov aggregation model
We consider a constrained version of the HL$(0)$ Hastings--Levitov model of aggregation in the complex plane, in which particles can only attach to the part of the cluster that has already been grown. Although one might expect that this gives rise to a non-trivial limiting shape, we prove that the cluster grows explosively: in the upper half plane, the aggregate accumulates infinite diameter as soon as it reaches positive capacity. More precisely, we show that after $nt$ particles of (half-plane) capacity $1/(2n)$ have attached, the diameter of the shape is highly concentrated around $\sqrt{t\log n}$, uniformly in $t\in [0,T]$. This illustrates a new instability phenomenon for the growth of single trees/fjords in unconstrained HL$(0)$.Open AccessExplosive growth for a constrained Hastings-Levitov aggregation model
We consider a constrained version of the HL$(0)$ Hastings--Levitov model of aggregation in the complex plane, in which particles can only attach to the part of the cluster that has already been grown. Although one might expect that this gives rise to a non-trivial limiting shape, we prove that the cluster grows explosively: in the upper half plane, the aggregate accumulates infinite diameter as soon as it reaches positive capacity. More precisely, we show that after $nt$ particles of (half-plane) capacity $1/(2n)$ have attached, the diameter of the shape is highly concentrated around $\sqrt{t\log n}$, uniformly in $t\in [0,T]$. This illustrates a new instability phenomenon for the growth of single trees/fjords in unconstrained HL$(0)$. - Open Access
- 11 June 2022
- Published by Springer Nature in Probability Theory and Related Fields
- Vol. 185 (1-2) , 185-250
Scaling limits for planar aggregation with subcritical fluctuations
We study scaling limits of a family of planar random growth processes in which clusters grow by the successive aggregation of small particles. In these models, clusters are encoded as a composition of conformal maps and the location of each successive particle is distributed according to the density of harmonic measure on the cluster boundary, raised to some power. We show that, when this power lies within a particular range, the macroscopic shape of the cluster converges to a disk, but that as the power approaches the edge of this range the fluctuations approach a critical point, which is a limit of stability. The methodology developed in this paper provides a blueprint for analysing more general random growth models, such as the Hastings-Levitov family.
- 11 June 2022
- Published by Springer Nature in Probability Theory and Related Fields
- Vol. 185 (1-2) , 185-250
Open AccessScaling limits for planar aggregation with subcritical fluctuations
We study scaling limits of a family of planar random growth processes in which clusters grow by the successive aggregation of small particles. In these models, clusters are encoded as a composition of conformal maps and the location of each successive particle is distributed according to the density of harmonic measure on the cluster boundary, raised to some power. We show that, when this power lies within a particular range, the macroscopic shape of the cluster converges to a disk, but that as the power approaches the edge of this range the fluctuations approach a critical point, which is a limit of stability. The methodology developed in this paper provides a blueprint for analysing more general random growth models, such as the Hastings-Levitov family.
- 3 November 2021
- Published by Springer Nature in Journal of Statistical Physics
- Vol. 185 (3) , 1-27
How Far do Activated Random Walkers Spread from a Single Source?
- 3 November 2021
- Published by Springer Nature in Journal of Statistical Physics
- Vol. 185 (3) , 1-27
How Far do Activated Random Walkers Spread from a Single Source?
- Open Access
Scaling limits for planar aggregation with subcritical fluctuations
We study scaling limits of a family of planar random growth processes in which clusters grow by the successive aggregation of small particles. In these models, clusters are encoded as a composition of conformal maps and the location of each successive particle is distributed according to the density of harmonic measure on the cluster boundary, raised to some power. We show that, when this power lies within a particular range, the macroscopic shape of the cluster converges to a disk, but that as the power approaches the edge of this range the fluctuations approach a critical point, which is a limit of stability. The methodology developed in this paper provides a blueprint for analysing more general random growth models, such as the Hastings-Levitov family.
Open AccessScaling limits for planar aggregation with subcritical fluctuations
We study scaling limits of a family of planar random growth processes in which clusters grow by the successive aggregation of small particles. In these models, clusters are encoded as a composition of conformal maps and the location of each successive particle is distributed according to the density of harmonic measure on the cluster boundary, raised to some power. We show that, when this power lies within a particular range, the macroscopic shape of the cluster converges to a disk, but that as the power approaches the edge of this range the fluctuations approach a critical point, which is a limit of stability. The methodology developed in this paper provides a blueprint for analysing more general random growth models, such as the Hastings-Levitov family.
- Open Access
How far do Activated Random Walkers spread from a single source?
Unlike many particle systems, Activated Random Walk has nontrivial behavior even in one spatial dimension. We prove inner and outer bounds on the spread of n activated random walkers from a single source in Z. The inner bound involves a comparison with the stationary distribution of activated random walkers on a finite interval, while the outer bound involves a comparison with the stabilization of an infinite Bernoulli configuration of activated random walkers on Z.
Open AccessHow far do Activated Random Walkers spread from a single source?
Unlike many particle systems, Activated Random Walk has nontrivial behavior even in one spatial dimension. We prove inner and outer bounds on the spread of n activated random walkers from a single source in Z. The inner bound involves a comparison with the stationary distribution of activated random walkers on a finite interval, while the outer bound involves a comparison with the stabilization of an infinite Bernoulli configuration of activated random walkers on Z.