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math.PR2026
The ergodic theory of SPDEs in a weak-noise regime
Mathew Joseph, Davar Khoshnevisan, Kunwoo Kim +1
Consider a parabolic SPDE \[ \partial_t u = Δu + σ(u)η, \] on , where is a centered, generalized Gaussian noise with $\text{Cov}[η(t\,,x)\,,η(s\…
math.PR2025
An Invariance Principle for some Reaction-Diffusion Equations with a Multiplicative Random Source
Davar Khoshnevisan, Kunwoo Kim, Carl Mueller
We establish a notion of universality for the parabolic Anderson model via an invariance principle for a wide family of parabolic stochastic partial differential equations. We then…
math.PR2023
Small-ball constants, and exceptional flat points of SPDEs
Davar Khoshnevisan, Kunwoo Kim, Carl Mueller
We study small-ball probabilities for the stochastic heat equation with multiplicative noise in the moderate-deviations regime. We prove the existence of a small-ball constant and…