Research Interests
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.
Publications and Preprints
- 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
Other publications and preprints
- Direct design of biquad filter cascades with deep learning by sampling random polynomials
preprint, submitted
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