Theo McKenzie I am an Assistant Professor in the Department of Statistics and Data Science at Yale University. I research the spectral geometry of discrete systems. Most often, this means studying random matrices and random graphs using analytic and probabilistic methods. More broadly, I am interested in questions in analysis and probability theory motivated by computer science and statistical physics. I am actively looking for Ph.D. students to join my group. If you are interested in working with me, please apply to our Ph.D. program and mention my name. If you are already at Yale, feel free to email me. My office is Kline Tower, Room 1053. E-mail: theo.mckenzie at yale.edu CV 2023-2026 I was a Stanford Science Fellow in the Department of Mathematics. 2022-2023, I was an NSF MPS-Ascend Postdoctoral Fellow at Harvard. 2017-2022, I was a Ph.D. student at UC Berkeley, where I was advised by Nikhil Srivastava and Luca Trevisan.

Research Papers

• The Gaussian Wave for Graphs of Finite Cone Type
  with Amir Dembo
  arxiv:2603.04386 Submitted


• Ramanujan Property and Edge Universality of Random Regular Graphs
  with Jiaoyang Huang and Horng-Tzer Yau
  arxiv:2412.20263 Submitted Quanta article


• Arbitrary Spectral Edge of Regular Graphs
  with Dingding Dong
  arxiv:2412.09570 to appear in Advances in Mathematics


• Optimal Eigenvalue Rigidity of Random Regular Graphs
  with Jiaoyang Huang and Horng-Tzer Yau
  arxiv:2405.12161 Permanent Draft


• The Spectral Edge of Constant Degree Erdős-Rényi Graphs
  with Ella Hiesmayr
  arXiv:2309.11007 Random Structures & Algorithms


• Nodal Decompositions of a Symmetrix Matrix
  with John Urschel
  arXiv:2305.10598 International Mathematics Research Notices


• Explicit Two-sided Unique-neighbor Expanders
  with Jun-Ting Hsieh, Sidhanth Mohanty, and Pedro Paredes
  arXiv:2302.01212 STOC 2024


• Quantum Ergodicity for Periodic Graphs
  with Mostafa Sabri
  arXiv:2208.12685 Commuications in Mathematical Physics


• Many Nodal Domains in Random Regular Graphs
  with Shirshendu Ganguly, Sidhanth Mohanty, and Nikhil Srivastava
  arXiv:2109.11532 Commuications in Mathematical Physics Slides


• The Necessity of Conditions for Graph Quantum Ergodicity and Cartesian Products with an Infinite Graph
  arXiv:2106.09772 Comptes Rendus Mathématique Slides


• Support of Closed Walks and Second Eigenvalue Multiplicity of Graphs
  with Peter Rasmussen and Nikhil Srivastava
  arXiv:2007.12819. STOC 2021 Slides


• High-girth Near-Ramanujan Graphs with Lossy Vertex Expansion
  with Sidhanth Mohanty
  arXiv:2007.13630. ICALP 2021


• A New Algorithm for the Robust Semi-random Independent Set Problem
  with Hermish Mehta and Luca Trevisan
  arXiv:1808.03633. SODA 2020 Slides

Expository Papers

• Predictive Policing: A Mathematical Primer
  Link
  with Joseph Johnson and Tian An Wong
  Notices of the AMS


• Real Stable Polynomials, Description and Application
  Undergraduate Thesis
  Advised by Péter Csikvári
  Harvard Mathematics Library

Teaching