While models of undirected and directed geometry in random i.i.d. disorder with rapidly decaying tails are expected to behave similarly and exhibit features of the Kardar--Parisi--Zhang universality class, the scenario when the background noise is fractal is expected to be significantly different. A canonical example o...
S. Ganguly, V. Ginsburg, Kai-Hao Jing· 0 citations
While the solution to the $1+1$ dimensional stochastic heat equation with multiplicative noise is closely related to the exponential of a Brownian motion, the two-dimensional picture exhibits an additional weak-to-strong disorder transition. In [CSZ'23], the critical two-dimensional stochastic heat flow (SHF) was const...
We study eigenvalues of discrete Schr\"odinger operators $H=\Delta+V$ on $\mathbb{Z}^2$, where $\Delta$ is the uncentered Laplacian, i.e., the un-normalized adjacency operator of $\mathbb{Z}^2$ and $V$ decays at infinity. By Weyl's theorem, the essential spectrum of $H$ is $[-4,4]$. We determine the sharp decay thresho...
S. Ganguly, Wen-Cai Liu· 0 citations
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