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
- The singularity probability of a random symmetric matrix is exponentially small
preprint
with Marcelo Campos, Matthew Jenssen, and Julian Sahasrabudhe
- Anti-concentration of random variables from zero-free regions
preprint
with Julian Sahasrabudhe
- Maximum entropy and integer partitions
preprint, submitted
with Gweneth McKinley and Will Perkins
- Singularity of random symmetric matrices revisited
preprint, submitted
with Marcelo Campos, Matthew Jenssen, and Julian Sahasrabudhe
- 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
- Success probability for selectively neutral invading species in the line model with a random fitness landscape
preprint, 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