Marcus Michelen

My research is in probability and combinatorics. A lot of my work involves using complex- and Fourier-analytic techniques in discrete settings.

• 41. A simple proof of local universality for roots of Kac polynomials

  preprint

  with Oren Yakir

• 40. A polynomial improvement for the odd cycle-complete Ramsey numbers

  preprint

  with Marcelo Campos, Matthew Jenssen, Florian Pfender and Julian Sahasrabudhe

• 39. Convergent points for random power series on the unit circle

  preprint

  with Mehtaab Sawhney

• 38. Law of large numbers for the discriminant of random polynomials

  preprint

  with Oren Yakir

• 37. A new lower bound for the Ramsey numbers R(3,k)

  preprint

  with Marcelo Campos, Matthew Jenssen and Julian Sahasrabudhe

• 36. Limit law for root separation in random polynomials

  preprint

  with Oren Yakir

• 35. On random locally flat-foldable origami

  preprint, submitted

  with Thomas Hull and Corrine Yap

• 34. The binomial random graph is a bad inducer

  preprint, submitted

  with Vishesh Jain and Fan Wei

• 33. Realizability of hypergraphs and high-dimensional contingency tables with random degrees and marginals

  preprint, under revision

  with Nicholas Christo

• 32. Entangled states are typically incomparable

  preprint, submitted

  with Vishesh Jain and Matthew Kwan

• 31. A new lower bound for sphere packing

  preprint, submitted

  with Marcelo Campos, Matthew Jenssen, and Julian Sahasrabudhe

• 30. Random polynomials: the closest roots to the unit circle

  preprint, submitted

  with Julian Sahasrabudhe

• 29. Central limit theorems and the geometry of polynomials

  Journal of the European Mathematical Society

  with Julian Sahasrabudhe

• 28. Age of gossip from connective properties via first passage percolation (2025)

  IEEE Transactions on Information Theory

  with Thomas Jacob Maranzatto

• 27. Potential-weighted connective constants and uniqueness of Gibbs measures (2025)

  Communications in Mathematical Physics

  with Will Perkins

• 26. Fluctuations in the logarithmic energy for zeros of random polynomials on the sphere (2024)

  Probability Theory and Related Fields

  with Oren Yakir

• 25. On random polynomials with an intermediate number of real roots (2024)

  Proceedings of the American Mathematical Society

  with Sean O'Rourke

• 24. The frog model on Galton-Watson trees (2024)

  Annals of Applied Probability

  with Josh Rosenberg

• 23. Almost sure behavior of the zeros of iterated derivatives of random polynomials (2024)

  Electronic Communications in Probability

  with Xuan-Truong Vu

• 22. Zeros of a growing number of derivatives of random polynomials with independent roots (2024)

  Proceedings of the American Mathematical Society

  with Xuan-Truong Vu

• 21. Sums of random polynomials with differing degrees (2024)

  Transactions of the American Mathematical Society

  with Isabelle Kraus and Sean O'Rourke

• 20. The singularity probability of a random symmetric matrix is exponentially small (2024)

  Journal of the American Mathematical Society

  with Marcelo Campos, Matthew Jenssen, and Julian Sahasrabudhe

• 19. The least singular value of a random symmetric matrix (2024)

  Forum of Mathematics, Pi

  with Marcelo Campos, Matthew Jenssen, and Julian Sahasrabudhe

• 18. Optimal mixing of the down-up walk on independent sets of a given size (2023)

  64th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2023)

  with Vishesh Jain, Huy Tuan Pham and Thuy-Duong Vuong

• 17. Quasipolynomial-time algorithms for Gibbs point processes (2023)

  Combinatorics, Probability and Computing

  with Matthew Jenssen and Mohan Ravichandran

• 16. Maximum entropy and integer partitions (2023)

  Combinatorial Theory

  with Gweneth McKinley and Will Perkins

• 15. Analyticity for classical gasses via recursion (2022)

  Communications in Mathematical Physics

  with Will Perkins

• 14. Strong spatial mixing for repulsive point processes (2022)

  Journal of Statistical Physics

  with Will Perkins

• 13. Direct design of biquad filter cascades with deep learning by sampling random polynomials (2022)

  The International Conference on Acoustics, Speech, & Signal Processing 2022

  Joseph T. Colonel, Christian J. Steinmetz, Marcus Michelen, Joshua D. Reiss

• 12. Anti-concentration of random variables from zero-free regions (2022)

  Discrete Analysis.

  with Julian Sahasrabudhe

• 11. Singularity of random symmetric matrices revisited (2022)

  Proceedings of the American Mathematical Society.

  with Marcelo Campos, Matthew Jenssen, and Julian Sahasrabudhe

• 10. Success probability for selectively neutral invading species in the line model with a random fitness landscape (2021)

  Studies in Applied Mathematics.

  with Suzan Farhang-Sardroodi, Natalia L. Komarova, and Robin Pemantle

• 9. Real roots near the unit circle of random polynomials (2021)

  Transactions of the American Mathematical Society

• 8. A characterization of polynomials whose high powers have non-negative coefficients (2020)

  Discrete Analysis

  with Julian Sahasrabudhe

• 7. Asymptotic bounds on graphical partitions and partition comparability (2020)

  International Mathematics Research Notices

  with Stephen Melczer and Somabha Mukherjee

• 6. Quenched Survival of Bernoulli Percolation on Galton-Watson Trees (2020)

  Journal of Statistical Physics

  with Robin Pemantle and Josh Rosenberg

• 5. The frog model on non-amenable trees (2020)

  Electronic Journal of Probability

  with Josh Rosenberg

• 4. A Short Note on the Average Maximal Number of Balls in a Bin (2020)

  Journal of Integer Sequences

• 3. Central limit theorems from the roots of probability generating functions (2019)

  Advances in Mathematics

  with Julian Sahasrabudhe

• 2. Critical Percolation and the Incipient Infinite Cluster on Galton-Watson Trees (2019)

  Electronic Communications in Probability

• 1. Invasion Percolation on Galton-Watson Trees (2019)

  Electronic Journal of Probability

  with Robin Pemantle and Josh Rosenberg

• La force du hasard [The power of chance]

  La Recherche

  Marcus Michelen, French translation by Philippe Pajot

• Automatic Origami Crease Pattern Generation from k-uniform Tilings

  Bridges 2023 Conference Proceedings

  David Goncharov, Marcus Michelen, Uyen Nguyen

• Folding Functions: Origami Corrugations from Equations

  Bridges 2019 Conference Proceedings

  Uyen Nguyen, Be Fritzson, Marcus Michelen