Research Interests

My current mathematical interests are in the intersection of probability,geometry, analysis and PDEs.

Papers

  1. R. Bañuelos, P. Mariano, J. Wang. Bounds for exit times of Brownian motion and the first Dirichlet eigenvalue for the Laplacian. Trans. Amer. Math. Soc. . 376 (2023), no. 08, 5409--543. arXiv:2003.06867

  2. P. Mariano, J. Wang. Spectral bounds for exit times on metric measure Dirichlet spaces and applications (submitted, 2022) arXiv:2211.05894

  3. P. Mariano, H. Panzo, J. Wang. Improved upper bounds for the Hot Spots constant of Lipschitz domains. Potential Anal. (2022) arXiv:2110.03672

  4. P. Mariano, H. Panzo. CLT with explicit variance for products of random singular matrices related to Hill's equation. Random Matrices: Theory Appl. 11 (2022), no. 02, 20 pp. arXiv:2012.02173

  5. Fabrice Baudoin, Maria Gordina, Phanuel Mariano, Gradient bounds for Kolmogorov type diffusions. Ann. Inst. Henry Poincare Probab. Stat. 56 (2020), no. 1, 612--636 arXiv:1803.01436

  6. Phanuel Mariano, Hugo Panzo, Conformal Skorokhod embeddings and related extremal problems. Electron. Commun. Probab. 25 (2020), paper no. 42, 11 pp. arXiv:2001.12008

  7. R. Majumdar, P. Mariano, H. Panzo, L. Peng and A. Sisti. Lyapunov exponent and variance for products of random matrices related to random Fibonacci sequences. Discrete Contin. Dyn. Syst. Ser. B. 25 (2020), 21 pp. arXiv:1809.02294"

  8. Fabrice Baudoin, Maria Gordina, Phanuel Mariano, On the Cheng-Yau gradient estimate for Carnot groups and sub-Riemannian manifolds. Proc. Amer. Math. Soc. 147 (2019), no.7. 3181--3189 arXiv:1809.07433

  9. A. Amiran, F. Baudoin, S. Brock, B. Coster, R. Craver, U. Ezeaka, P. Mariano and M. Wishart, The financial value of knowing the distribution of stock prices in discrete market models , Involve, 12 (2019), no.5. 883--889 arXiv:1809.02294"

  10. Banerjee, Sayan; Gordina, Maria; Mariano, Phanuel. Coupling in the Heisenberg group and its applications to gradient estimates. Ann. Probab. 46 (2018), no. 6, 3275--3312. arXiv:1610.06430

  11. Phanuel Mariano, On the Coarse Geometry of Lp, Rose-Hulman Undergraduate Math Journal Vol. 14 , No. 2 (2013)

Other

  1. R. Majumdar, P. Mariano, L. Peng and A. Sisti. A Derivation of the Black-Scholes Option Pricing Model Using a Central Limit Argument. arXiv:1804.03290

Funding

    PI - NSF grant DMS-2316968, 2023-2025
  • PI - AMS-Simons Travel Grant, 2019-2023
  • PI - NSF grant, 2022 Union College Mathematics Conference, DMS-2154896, 2022.
  • Spring research was supported in part by NSF Grant DMS-1405169, 2018.
  • Summer research was supported in part by NSF Grant DMS-1262929, 2017.
  • Summer research was supported in part by NSF Grant DMS-1007496, 2016.