7 problems

Skew Brownian LIS exponent conjecture. There exists a function $\ell:[-1,1]\times(0,1)\to[1/2,1)$ such that, with probability tending to $1$ as $n\to\infty$,

Discrete–continuum exponent conjecture. With probability tending to $1$ as $n\to\infty$,

Let $t_n$ be a uniformly sampled tree of size approximately $n$ in the square-torus uniform spanning-tree model, and let $w(t_n)$ be its Euclidean width. The UST width exponent con…

Let ${\sf TDLA}_0(n,[0,+\infty)^2)$ be the square DLA tree with $n$ vertices, rooted at the corner ${\bf c}$, and let ${\bf v}$ be a uniformly sampled vertex of the tree. Write…

Let $R$ be the renormalisation transformation on point fields of concentration points and shocks, and suppose the density decays as $n^{-\alpha}$ for a critical exponent…

Antal and Krapivsky's conjecture. For each $k=1,\ldots,K$, the expected number of individuals of type $k$ satisfies

Let $E(t)={\mathbf E}(X(t)^2)$, and suppose that for some $-1<\alpha<1$ the infrared bounds … hold. Diffusivity exponent conjecture. Under these conditions, the true asymptotic ord…