Interests
- Random processes in random media;
- Random graphs;
- Mathematics of Neural Networks;
- Stochastic homogenization;
- Mixing times for Markov chains;
- Statistical mechanics.
Preprints
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F. Angileri, A. Clementi, E. Natale, M. Salvi, I. Ziccardi
Threshold-driven streaming graph: Expansion and rumor spreading
arXiv preprint (2025). -
A. Barnier, P. Hoscheit, M. Salvi, E. Vergu
The contact process on Scale-Free Percolation
arXiv preprint (2025). -
S. Di Lillo, D. Marinucci, M. Salvi, S. Vigogna
Fractal and Regular Geometry of Deep Neural Networks
arXiv preprint (2025). -
A. Cipriani, R. S. Hazra, N. Malhotra, M. Salvi
The spectrum of dense kernel-based random graphs
arXiv preprint (2025). -
L. Makowiec, M. Salvi, R. Sun
Random spanning trees in random environment
arXiv preprint (2024).
Journal articles
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[J15] S. Di Lillo, D. Marinucci, M. Salvi, S. Vigogna
Spectral complexity of deep neural networks
SIAM Journal on Mathematics of Data Science (SIMODS) (2025). -
[J14] L. Makowiec, M. Salvi, R. Sun
Diameter of uniform spanning trees on random weighted graphs
To appear in Annales de l’Institut Henri Poincaré - Probabilit\'s et Statistiques (2024+). -
[J13] V. Cammarota, D. Marinucci, M. Salvi, S. Vigogna
A quantitative functional central limit theorem for shallow neural networks
Modern Stochastics: Theory and Applications, 11, 85-108 (2024). -
[J12] V. Bansaye, M. Salvi,
Branching process and homogeneization for epidemics on spatial random graphs
Electronic Journal of Probability, 29: 1-37 (2024). -
[J11] A. Cipriani, M. Salvi,
Scale-free percolation mixing time
Stochastic Processes and their Applications, 167 (2024). -
[J10] Q. Berger, M. Salvi,
Scaling limit of sub-ballistic 1D random walk among biased conductances: a story of wells and walls
Electronic Journal of Probability, 25: 1-43 (2020). -
[J9] J. Dalmau, M. Salvi,
Scale-free percolation in continuum space: quenched degree and clustering coefficient
Journal of Applied Probability, Volume 58, Issue 1, 106 - 127 (2021), arXiv preprint. -
[J8] A. Faggionato, M. Salvi,
Regularity of biased 1D random walks in random environment
ALEA Lat. Am. J. Probab. Math. Stat. , 16, 1213-1248 (2019). -
[J7] Q. Berger, M. Salvi,
Scaling of sub-ballistic 1d random walks among biased random conductances
Markov processes and Related Fields, Volume 25, Issue 1, 171-187 (2019), arXiv preprint. -
[J6] A. Faggionato, N. Gantert , M. Salvi,
Einstein relation and linear response in one-dimensional Mott variable-range hopping
Annales de l’Institut Henri Poincaré - Probabilités et Statistiques, 55(3): 1477-1508 (2019). -
[J5] F. Simenhaus , M. Salvi,
Random walk on a perturbation of the infinitely-fast mixing interchange process
Journal of Statistical Physics, 171(4), 656-678 (2018). -
[J4] A. Faggionato, N. Gantert , M. Salvi,
The velocity of 1D Mott variable range hopping with external field
Annales de l’Institut Henri Poincaré - Probabilités et Statistiques, Volume 54, Number 3, 1165-1203 (2018). -
[J3] M. Biskup, M. Salvi, T. Wolff,
A central limit theorem for the effective conductance: I. Linear boundary data and small ellipticity contrasts
Commununications in Mathematical Physics, 328, no. 2, 701-731 (2014), arXiv preprint. -
[J2] N. Berger, M. Salvi,
On the speed of random walks among random conductances
ALEA Lat. Am. J. Probab. Math. Stat., Vol. X, 1063-1083 (2013). -
[J1] W. König, M. Salvi, T. Wolff,
Large deviations for the local times of a random walk among random conductances
Electronic Communications in Probability, 17 (2011).
Conference papers
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[C1] F. Angileri, G. Lombardi, A. Fois, R. Faraone, C. Metta, M. Salvi, L.A. Bianchi, M. Fantozzi, S.g. Galfrè, D. Pavesi, M. Parton, F. Morandin
A Systematization of the Wagner Framework: Graph Theory Conjectures and Reinforcement Learning
Discovery Science. DS 2024. Lecture Notes in Computer Science, vol 15243. Springer, (2025), arXiv preprint.
PhD Thesis
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M. Salvi,
The Random Conductance Model: Local times large deviations, law of large numbers and effective conductance
Ph.D. Thesis.
Talks and slides
More
- A Central Limit Theorem for the Effective Conductance (2012), poster for the conference Interacting Particle Systems and Related Topics, Firenze.
- On the speed of Random Walks among Random Conductances (2012), long abstract, in Oberwolfach Reports.
- The Cut-off phenomenon for Monte Carlo Markov chains (2009), master thesis.