Research

I am mainly interested in Probability Theory and its interactions with other disciplines, such as Geometry, Algebra and Analysis. Indeed, my main research topics concern

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

Published (or to appear) papers

  • G. Peccati, M. Rossi: Quantitative limit theorems for local functionals of arithmetic random waves. To appear in The Abel Symposium 2016. ArXiv file.
  • 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.
  • 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.
  • 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
  • P. Baldi, M. Rossi: Representation of Gaussian isotropic spin random fields. Stochastic Processes and their Applications, 124, 5, 1910-1941 (2014). Article
  • P. Baldi, M. Rossi: On Levy’s Brownian motion indexed by elements of compact groups. Colloquium Mathematicum, 133, 227-236 (2013). Article

Preprint

  • I. Nourdin, G. Peccati, M. Rossi: Nodal statistics of planar random waves. Submitted. ArXiv file.
  • D. Marinucci, M. Rossi, I. Wigman: The asymptotic equivalence of the sample trispectrum and the nodal length for random spherical harmonics. Submitted. ArXiv file.
  • M. Rossi, I. Wigman: Asymptotic distribution of nodal intersections for arithmetic random waves. Submitted. ArXiv file.
  • F. Dalmao, I. Nourdin, G. Peccati, M. Rossi: Phase singularities in complex arithmetic random waves. Submitted. ArXiv file.
  • M. Rossi: The defect of random hyperspherical harmonics. Submitted. ArXiv file.
  • S. Campese, D. Marinucci, M. Rossi: Approximate normality for high-energy hyperspherical eigenfunctionsSubmitted. ArXiv file.
  • P. Baldi, L. Caramellino, M. Rossi: Large Deviation asymptotics for the exit from a domain of the bridge of a general Diffusion. ArXiv file.

Conference Proceedings

  • 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.

Others

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

 

My Erdös number is 3.

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