Dr. Leonardo Tolomeo

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School of Mathematics, University of Edinburgh 		Mailing address:
School of Mathematics
The University of Edinburgh,
James Clerk Maxwell Building, Room 5405
The King's Buildings, Peter Guthrie Tait Road
Edinburgh, EH9 3FD, United Kingdom
Office: Room 5405
E-mail: l.tolomeo ατ ed.ac.uk
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Publications:

Published and accepted papers:

  1. (with A. Martini, F. Ricci) Convolution kernels versus spectral multipliers for sub-Laplacians on groups of polynomial growth, J. Funct. Anal. 277 (2019), no. 6, 1603–1638.
  2. (with A. Amenta) A dichotomy concerning uniform boundedness of Riesz transforms on Riemannian manifolds, Proc. Amer. Math. Soc. 147 (2019), no. 11, 4797–4803.
  3. Unique ergodicity for a class of stochastic hyperbolic equations with additive space-time white noise, Comm. Math. Phys. 377 (2020), no. 2, 1311–1347.
  4. Global well-posedness of the two-dimensional stochastic nonlinear wave equation on an unbounded domain, Ann. Probab. (2021), no. 3, 1402–1426.
  5. (with M. Gubinelli, H. Koch, T. Oh) Global dynamics for the two-dimensional stochastic nonlinear wave equations, Int. Math. Res. Not. IMRN (2022), no. 21, 16954–16999.
  6. (with V. Cavina, P.A. Erdman, P. Abiuso, V. Giovannetti) Maximum power heat engines and refrigerators in the fast-driving regime, Phys. Rev. A (2021), no. 3, Paper No. 032226, 22 pp.
  7. (with T. Oh, P. Sosoe) Optimal integrability threshold for Gibbs measures associated with focusing NLS on the torus, Invent. Math. 227 (2022), no. 3, 1323–1429.
  8. (with J. Forlano) On the unique ergodicity for a class of 2 dimensional stochastic wave equations, Trans. Amer. Math. Soc. 377 (2024), no. 1, 345–394.
  9. (with T. Oh, K. Seong) A remark on Gibbs measures with log-correlated Gaussian fields, Forum Math. Sigma (2024), Paper No. e50, 40 pp.
  10. (with T. Oh, M. Okamoto) Focusing Φ43-model with a Hartree-type nonlinearity, arXiv:2009.03251, Mem. Amer. Math. Soc. 304 (2024), no. 1529, vi+143 pp.
  11. (with T. Robert, K. Seong, Y. Wang) Focusing Gibbs measures with harmonic potential, arXiv:2212.11386, Ann. Inst. Henri Poincaré Probab. Stat. 61 (2025), no. 1, 571–598.
  12. (with T. Oh, M. Okamoto) Stochastic quantization of the Φ33-model, Mem. Eur. Math. Soc., 16 EMS Press, Berlin, 2025, viii+145 pp.
  13. (with J. Forlano) Quasi-invariance of Gaussian measures of negative regularity for fractional nonlinear Schrödinger equations, arXiv:2205.11453, to appear in J. Eur. Math. Soc. (JEMS).
  14. (with D. Greco, T. Oh, L. Tao) Critical threshold for weakly interacting log-correlated focusing Gibbs measures, Proc. Amer. Math. Soc. Ser. B 12 (2025), 150–165.
  15. (with J. Coe) Sharp quasi-invariance threshold for the cubic Szegő equation, arXiv:2404.14950, to appear in Anal. PDE.
  16. (with T. Oh, Y. Wang, G. Zheng) Hyperbolic P(Φ)2-model on the plane, arXiv:2211.03735, Comm. Math. Phys. 407 (2026), no. 2, Paper No. 34, 84 pp.
  17. (with H. Weber) Phase transition for invariant measures of the focusing Schrödinger equation, Comm. Math. Phys. 407, 82 (2026).
  18. (with J. Forlano) Quasi-invariance of the Gaussian measure for the two-dimensional stochastic cubic nonlinear wave equation, arXiv:2409.20451, to appear in Stoch. Partial Differ. Equ. Anal. Comput., special volume in honour of G. da Prato.
  19. (with M. Romito) Yet another notion of irregularity through small ball estimates, arXiv:2207.02716, Stochastic Process. Appl. 195 (2026), Paper No. 104895, 43 pp.
  20. (with V. D. Dinh, N. Rougerie, Y. Wang) Statistical mechanics of the radial focusing nonlinear Schrödinger equation in general traps, arXiv:2312.06232, to appear in Math. Ann.
  21. (with G. Li, J. Li) A remark on the log-Sobolev inequality for the Gibbs measure of the focusing Schrödinger equation, arXiv:2512.03897, to appear in J. Dynam. Differential Equations.
  22. (with Y. Bruned) Cancellations for dispersive PDEs with random initial data, arXiv:2412.17051, to appear in Prob. Math. Phys.

Preprints:

  1. Ergodicity for the hyperbolic P(Φ)2-model, arXiv:2310.02190.
  2. (with J. Coe, M. Hairer) Quasi-Gaussianity of the 2D stochastic Navier-Stokes equations, arXiv:2510.13460.
  3. (with N. Visciglia) Quasi invariant Gaussian measures for the nonlinear Schrödinger equation on 𝕋2, arXiv:2512.13113.