Author

Kunwoo Kim

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Preprint Sep 2026

Limit theorems for the one-dimensional parabolic Anderson model with white noise potential

We consider the parabolic Anderson model $\partial_t u=\partial_x^2 u+\xi u$ on $\mathbb{R}_+\times\mathbb{R}$ with $u(0,\cdot)\equiv 1$, where $\xi$ is a spatial white noise. We study the long-time behavior of the spatial integral $U(t):=\int_{-L(t)/2}^{L(t)/2}u(t,x)\,dx$, where $L(t)=\exp(\alpha^3 t^3/24)$ with $\alp...

Kunwoo Kim, U. Kim, J. Yi · 0 citations

Preprint Sep 2026

Instantaneous shrinking of supports for stochastic PDEs

We study instantaneous shrinking of supports for nonnegative solutions of the stochastic partial differential equation \[ \partial_t u=a(t,x)\,\partial_x^2 u + b(t,x)\,\partial_x u + c(t,x)\,u +\sigma(u)\,\xi(t,x), \qquad (t,x)\in(0,\infty)\times\mathbb R, \] where $\xi$ is space-time white noise, the coefficients $a$,...

B. Han, Kunwoo Kim, J. Yi · 1 citation