Research Interests
My research is in probability, combinatorics, and the geometry of polynomials. Much my research concerns probabilistic and extremal properties of polynomials as well as stochastic spatial processes such as percolation, interacting random walk and Gibbs point processes.
Publications and Preprints
- Maximum entropy and integer partitions
preprint
with Gweneth McKinley and Will Perkins
- Singularity of random symmetric matrices revisited
preprint, submitted
with Marcelo Campos, Matthew Jenssen, and Julian Sahsrabudhe
- Random polynomials: the closest roots to the unit circle
preprint, submitted
with Julian Sahsrabudhe
- Analyticity for classical gasses via recursion
preprint, submitted
with Will Perkins
- The frog model on Galton-Watson trees
preprint, submitted
with Josh Rosenberg
- Success probability for selectively neutral invading species in the line model
preprint, submitted
with with Suzan Farhang-Sardroodi, Natalia L. Komarova, and Robin Pemantle
- Central limit theorems and the geometry of polynomials
preprint, submitted
with Julian Sahasrabudhe
- Real roots near the unit circle of random polynomials
Accepted to Transactions of the AMS
- 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