9 problems

Outside-cone fluctuation conjecture. If

Axial curvature and fluctuation exponent conjecture. For $r>0$,

Transversal fluctuation exponent conjecture. The observation that the oriented-percolation example rules out the assertion $\xi(u)=2/3$ for every $u$ shows that this proposed unive…

Let $p<p_c(2)$, where $p_c(2)$ is the critical probability for Bernoulli bond percolation on ${\bf Z}^2$. Let $B_2$ be the unit ball of the time-constant norm, let…

Let $h_L$ be the solution to the KPZ equation on a torus of size $L$ in dimension $d=1$, driven by noise that is white in time and has spatial covariance function $R$ independent o…

Anisotropic KPZ conjecture. If the Hessian matrix $D^2v(\rho)$ has two eigenvalues of the same sign, equivalently if $\det(D^2v(\rho))>0$, then

Let $\xi$ be the transversal fluctuation exponent and let $\xi'$ denote the related transversal fluctuation exponent introduced in the source. Transversal exponent equality conject…

Let $\chi'(v)$ be the fluctuation exponent associated with a direction $v\in S^{d-1}$, and let $\chi$ be the usual fluctuation exponent. Direction-independence conjecture. The expo…

Let $Z_n$ be the partition function of a directed polymer of length $N$, and let $Q$ denote the disorder expectation. Suppose that the fluctuation exponents $xi>0$ and…