5 problems

The $t^{1/3}$ superdiffusivity conjecture. In particular, there is a constant $C$ such that

Beijeren–Kutner–Spohn conjecture. Based on mode-coupling theory, the diffusion coefficient satisfies $D(t)\sim(\log t)^{2/3}$ in dimension $d=2$ and $D(t)\sim t^{1/3}$ in dimension…

Let $X(t)$ be the position of the Brownian particle in the curl of the two-dimensional Gaussian free field, and define its Laplace-transformed mean square displacement by … The cor…

Let $H$ be the stationary solution of the two-dimensional anisotropic KPZ equation, whose nonlinearity is $(\partial_1 H)^2-(\partial_2 H)^2$, and let $\delta\in(0,1)$ be an expone…

Let $B=(B_s)_{s\in[0,t]}$ be the polymer trajectory distributed according to the polymer measure $\mu_t$, and let $\|B_s\|$ denote its distance from the origin. Superdiffusivity co…