Marcus Michelen

My research is in probability, combinatorics and classical analysis. A lot of my work involves using complex- and Fourier-analytic techniques in discrete settings. Specific recent projects include random algebraic structures such as matrices, polynomials and partitions; the relationship between zero-free regions and probability theory; and Gibbs point processes.

• The least singular value of a random symmetric matrix

  preprint, submitted

  with Marcelo Campos, Matthew Jenssen, and Julian Sahasrabudhe

• Strong spatial mixing for repulsive point processes

  preprint, submitted

  with Will Perkins

• Potential-weighted connective constants and uniqueness of Gibbs measures

  preprint, submitted

  with Will Perkins

• The singularity probability of a random symmetric matrix is exponentially small

  preprint, submitted

  with Marcelo Campos, Matthew Jenssen, and Julian Sahasrabudhe

• Anti-concentration of random variables from zero-free regions

  preprint, submitted

  with Julian Sahasrabudhe

• Maximum entropy and integer partitions

  preprint, submitted

  with Gweneth McKinley and Will Perkins

• Random polynomials: the closest roots to the unit circle

  preprint, submitted

  with Julian Sahasrabudhe

• Analyticity for classical gasses via recursion

  preprint, submitted

  with Will Perkins

• The frog model on Galton-Watson trees

  preprint, submitted

  with Josh Rosenberg

• Central limit theorems and the geometry of polynomials

  preprint, submitted

  with Julian Sahasrabudhe

• Singularity of random symmetric matrices revisited

  To appear, Proceedings of the American Mathematical Society.

  with Marcelo Campos, Matthew Jenssen, and Julian Sahasrabudhe

• Success probability for selectively neutral invading species in the line model with a random fitness landscape

  Studies in Applied Mathematics.

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

• Real roots near the unit circle of random polynomials

  Transactions of the American Mathematical Society

• A characterization of polynomials whose high powers have non-negative coefficients

  Discrete Analysis

  with Julian Sahasrabudhe

• Asymptotic bounds on graphical partitions and partition comparability

  International Mathematics Research Notices

  with Stephen Melczer and Somabha Mukherjee

• Quenched Survival of Bernoulli Percolation on Galton-Watson Trees

  Journal of Statistical Physics

  with Robin Pemantle and Josh Rosenberg

• The frog model on non-amenable trees

  Electronic Journal of Probability

  with Josh Rosenberg

• A Short Note on the Average Maximal Number of Balls in a Bin

  Journal of Integer Sequences

• Central limit theorems from the roots of probability generating functions

  Advances in Mathematics

  with Julian Sahasrabudhe

• Critical Percolation and the Incipient Infinite Cluster on Galton-Watson Trees

  Electronic Communications in Probability

• Invasion Percolation on Galton-Watson Trees

  Electronic Journal of Probability

  with Robin Pemantle and Josh Rosenberg

• Direct design of biquad filter cascades with deep learning by sampling random polynomials

  preprint, to appear in ICASSP 2022

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

• Folding Functions: Origami Corrugations from Equations

  Bridges 2019 Conference Proceedings

  Uyen Nguyen, Ben Fritzson, Marcus Michelen