Interests

  • Random processes in random media;
  • Random graphs;
  • Mathematics of Neural Networks;
  • Stochastic homogenization;
  • Mixing times for Markov chains;
  • Statistical mechanics.

Publications and preprints

  1. [20] S. Di Lillo, D. Marinucci, M. Salvi, S. Vigogna
    Fractal and Regular Geometry of Deep Neural Networks
    arXiv preprint (2025).
  2. [19] A. Cipriani, R. S. Hazra, N. Malhotra, M. Salvi
    The spectrum of dense kernel-based random graphs
    arXiv preprint (2025).
  3. [18] L. Makowiec, M. Salvi, R. Sun
    Random spanning trees in random environment
    arXiv preprint (2024).
  4. [17] 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.
  5. [16] S. Di Lillo, D. Marinucci, M. Salvi, S. Vigogna
    Spectral complexity of deep neural networks
    Accepted for publication in SIAM Journal on Mathematics of Data Science (SIMODS), arXiv preprint (2024).
  6. [15] 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+).
  7. [14] 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).
  8. [13] V. Bansaye, M. Salvi,
    Branching process and homogeneization for epidemics on spatial random graphs
    Electronic Journal of Probability, 29: 1-37 (2024).
  9. [12] A. Cipriani, M. Salvi,
    Scale-free percolation mixing time
    Stochastic Processes and their Applications, 167 (2024).
  10. [11] 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).
  11. [10] 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.
  12. [9] A. Faggionato, M. Salvi,
    Regularity of biased 1D random walks in random environment
    ALEA Lat. Am. J. Probab. Math. Stat. , 16, 1213-1248 (2019).
  13. [8] 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.
  14. [7] A. Faggionato, N. Gantert , M. Salvi,
    Einstein relation and linear response in one-dimensional Mott variable-range hopping
    Annales de l’Institut Henri Poincaré - Probabilit\'s et Statistiques, 55(3): 1477-1508 (2019).
  15. [6] 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).
  16. [5] A. Faggionato, N. Gantert , M. Salvi,
    The velocity of 1D Mott variable range hopping with external field
    Annales de l’Institut Henri Poincaré - Probabilit\'s et Statistiques, Volume 54, Number 3, 1165-1203 (2018).
  17. [4] M. Salvi,
    The Random Conductance Model: Local times large deviations, law of large numbers and effective conductance
    Ph.D. Thesis.
  18. [3] 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.
  19. [2] 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).
  20. [1] 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).

Talks and slides

  1. Scale-Free Percolation Mixing Time ,
    Pavia-Milano Seminar series on Probability and Mathematical Statistics, May 2022.
  2. The Einstein Relation for the Mott Variable-Range Hopping model ,
    Séminaires Probabilités, École Polytechnique, January 2018. [PDF]
    Séminaires Probabilités, UPEC, Paris, December 2017.
    SPA, Moscow, June 2017.
  3. On the speed of random walks among random conductances,
    UCLA probability seminars, Los Angeles, April 2012 [PDF]
    LATP Séminaires de Probabilités et statistiques, CIRM, Marseille, February 2013.
  4. Law of large numbers for the Mott Variable Range Hopping model,
    World Congress in Probability, Toronto, July 2016 [PDF]
    Séminaires Analyse-Probabilités, Université Paris-Dauphine, October 2016.
  5. On the speed of random walks among random conductances,
    UCLA probability seminars, Los Angeles, April 2012 [PDF]
    LATP Séminaires de Probabilités et statistiques, CIRM, Marseille, February 2013.
  6. On the speed of random walks among random conductances (in five minutes!),
    Workshop: Interaction between analysis and probability in Physics, Oberwolfach, February 2012 [PDF]
  7. A large deviation principle for a RWRC in a box (short version),
    7th Cornell Probability Summer School, Cornell University, July 2011 [PDF]
  8. A large deviation principle for a RWRC in a box (complete version),
    IRTG seminars, Berlin, February 2011 [PDF]
  9. The Cut-off Phenomenon for Monte Carlo Markov Chains,
    IRTG interview, Berlin, February 2010 [PDF]

More

  1. A Central Limit Theorem for the Effective Conductance (2012), poster for the conference Interacting Particle Systems and Related Topics, Firenze.
  2. On the speed of Random Walks among Random Conductances (2012), long abstract, in Oberwolfach Reports.
  3. The Cut-off phenomenon for Monte Carlo Markov chains (2009), master thesis.