Qiang Zeng

Welcome to my homepage! I am a probabilist working in spin glasses and noncommutative probability. I am also broadly interested in probability theory, functional analysis, and mathematical physics. You can reach me at qzeng.math AT gmail.com.

Papers

• On the expected number of critical points of locally isotropic Gaussian random fields, (with Hao Xu and Haoran Yang).
  Submitted. [arXiv]

• Hessian spectrum at the global minimum and topology trivialization of locally isotropic Gaussian random fields, (with Hao Xu).
  Submitted. [arXiv]

• Complexity of Gaussian random fields with isotropic increments: critical points with given indices, (with Antonio Auffinger).
  Submitted. [arXiv]

• Complexity of Gaussian random fields with isotropic increments, (with Antonio Auffinger).
  Communications in Mathematical Physics, 402(1): 951–993 (2023). [arXiv]  [journal]

• Existence of two-step replica symmetry breaking for the spherical mixed p-spin glass at zero temperature, (with Antonio Auffinger).
  Communications in Mathematical Physics, 370(1): 377–402 (2019). [arXiv]  [journal]

• The SK model is infinite step Replica Symmetry Breaking at zero temperature, (with Antonio Auffinger and Wei-Kuo Chen).
  Communications on Pure and Applied Mathematics, 73(5): 921–943 (2020). [arXiv]  [journal]

• Harmonic analysis approach to Gromov--Hausdorff convergence for noncommutative tori, (with Marius Junge and Sepideh Rezvani).
  Communications in Mathematical Physics, 358(3): 919–994 (2018). [arXiv]  [journal]

• Free monotone transport for infinite variables, (with Brent Nelson).
  International Mathematics Research Notices, 2018(17): 5486–5535 (2018). [arXiv]  [journal]

• An application of free transport to mixed q-Gaussian algebras, (with Brent Nelson).
  Proceedings of the American Mathematical Society, 144(10): 4357–4366 (2016). [arXiv]  [journal]

• Ultraproduct methods for mixed q-Gaussian algebras, (with Marius Junge).
  Submitted. [arXiv]

• Subgaussian 1-cocycles on discrete groups, (with Marius Junge).
  Journal of the London Mathematical Society, 92(2): 242–264 (2015). [arXiv]  [journal]

• Poincaré type inequalities for group measure spaces and related transportation cost inequalities.
  Journal of Functional Analysis, 266(5): 3236–3264 (2014). [arXiv]  [journal]

• Kolmogorov's law of the iterated logarithm for noncommutative martingales.
  Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 51(3): 1124–1130 (2015). [arXiv]  [journal]

• Noncommutative martingale deviation and Poincaré type inequalities with applications, (with Marius Junge).
  Probability Theory and Related Feilds, 161(3-4): 449–507 (2015). [arXiv]  [journal]

• Noncommutative Bennett and Rosenthal inequalities, (with Marius Junge).
  Annals of Probability, 41(6): 4287–4316 (2013). [arXiv]  [journal]