3 citations · 4 across the 5 of their papers we have counts for
6 papers
Separation of time scales in weakly interacting diffusions
Zachary P. Adams, Maximilian Engel, Rishabh S. Gvalani
We study metastable behaviour in systems of weakly interacting Brownian particles with localised, attractive potentials which are smooth and globally bounded. In this particular se…
Meta-Posterior Consistency for the Bayesian Inference of Metastable System
Zachary P Adams, Sayan Mukherjee
The vast majority of the literature on learning dynamical systems or stochastic processes from time series has focused on stable or ergodic systems, for both Bayesian and frequenti…
The Isochronal Phase of Stochastic PDE and Integral Equations: Metastability and Other Properties
Zachary P. Adams, James MacLaurin
We study the dynamics of waves, oscillations, and other spatio-temporal patterns in stochastic evolution systems, including SPDE and stochastic integral equations. Representing a g…
Quasi-Ergodicity of Transient Patterns in Stochastic Reaction-Diffusion Equations
Zachary P. Adams
We study transient patterns appearing in a class of SPDE using the framework of quasi-stationary and quasi-ergodic measures. In particular, we prove the existence and uniqueness of…
Existence, Regularity, and a Strong Itô Formula for the Isochronal Phase of SPDE
Zachary P. Adams
We prove the existence and regularity of the isochron map for stable invariant manifolds of a large class of evolution equations. Our results apply in particular to the isochron ma…
The asymptotic frequency of stochastic oscillators
Zachary P. Adams
We study stochastic perturbations of ODE with stable limit cycles -- referred to as stochastic oscillators -- and investigate the response of the asymptotic (in time) frequency of…