I am mainly interested in Probability Theory and Mathematical Statistics and their interactions with other disciplines. Indeed, my main research topics concern

  • Geometrical properties of random eigenfunctions on manifolds
  • Random fields on algebraic structures
  • Probabilistic approximations
  • Large Deviations for diffusion processes and applications
  • Statistical inference for random fields

Published (or to appear) papers

  1. D. Marinucci, M. Rossi, I. Wigman: The asymptotic equivalence of the sample trispectrum and the nodal length for random spherical harmonics. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques (in press). Article.
  2. M. Rossi: The defect of random hyperspherical harmonics. Journal of Theoretical Probability (in press). Article.
  3. M. Rossi, I. Wigman: Asymptotic distribution of nodal intersections for arithmetic random waves. Nonlinearity, 31, 4472 (2018). Article.
  4. G. Peccati, M. Rossi: Quantitative limit theorems for local functionals of arithmetic random waves. Computation and Combinatorics in Dynamics, Stochastics and Control, The Abel Symposium, Rosendal, Norway, August 2016, 13, 659-689 (2018). Article.
  5. S. Campese, D. Marinucci, M. Rossi: Approximate normality of high-energy hyperspherical eigenfunctions. Journal of Mathematical Analysis and Applications, 461, 1, 500–522 (2018). Article.
  6. D. Marinucci, G. Peccati, M. Rossi, I. Wigman: Non-universality of nodal length distribution for arithmetic random wavesGeometric and Functional Analysis, 26, 3, 926–960 (2016). Article.
  7. P. Baldi, L. Caramellino, M. Rossi: On Sharp Large Deviations for the bridge of a general Diffusion. In memoriam Marc YorSéminaire de Probabilités XLVII, Lecture Notes in Mathematics, 2137, 427-441 (2015). Article.
  8. D. Marinucci, M. Rossi: Stein-Malliavin approximations for nonlinear functionals of random eigenfunctions on S^dJournal of Functional Analysis, 268, 8, 2379-2420 (2015). Article
  9. P. Baldi, M. Rossi: Representation of Gaussian isotropic spin random fields. Stochastic Processes and their Applications, 124, 5, 1910-1941 (2014). Article
  10. P. Baldi, M. Rossi: On Levy’s Brownian motion indexed by elements of compact groups. Colloquium Mathematicum, 133, 227-236 (2013). Article


  1. P. Baldi, L. Caramellino, M. Rossi: Large Deviations of conditioned diffusions and applications. Submitted
  2. G. Dierickx, I. Nourdin, G. Peccati, M. Rossi: Small scale CLTs for nodal length of monochromatic waves. Working paper.
  3. I. Nourdin, G. Peccati, M. Rossi: Nodal statistics of planar random waves. Submitted. ArXiv file.
  4. F. Dalmao, I. Nourdin, G. Peccati, M. Rossi: Phase singularities in complex arithmetic random waves. Submitted. ArXiv file.

Conference Proceedings

  1. M. Rossi: Random nodal lengths and Wiener chaos. Proceedings of the Workshop “Probabilistic Methods in Spectral Geometry and PDE” in Montréal, August 2016 (to appear). ArXiv file.
  2. M. Rossi: On the high-energy behavior of nonlinear functionals of random eigenfunctions on S^dProceedings of the “19th EYSM in Prague”, 119-124 (2015). ArXiv file.


  1. M. Rossi: The geometry of spherical random fields. PhD Thesis, University of Rome “Tor Vergata” (2015). ArXiv file.


My Erdös number is 3.