3 papers
math.PR2026
Persistent anisotropy in multi-dimensional branching Brownian motion
Cole Graham, Leonid Mytnik, Lenya Ryzhik
We study angular variation in the frontier of branching Brownian motion (BBM) in multiple dimensions. The time average of this frontier is tied to the long-time limit of the critic…
math.PR2026
Renormalization flow for the 2D nonlinear stochastic heat equation: pointwise statistics and universality
Alexander Dunlap, Cole Graham
We consider a two-dimensional stochastic heat equation with noise correlated at scale and of strength depending nonlinearly on the solution . Un…
math.PR2025
Stationary solutions to the stochastic Burgers equation on the line
Alexander Dunlap, Cole Graham, Lenya Ryzhik
We consider invariant measures for the stochastic Burgers equation on , forced by the derivative of a spacetime-homogeneous Gaussian noise that is white in time and smo…