17 problems

The flat PNG model has a height function whose fluctuations are governed by the GOE Tracy–Widom distribution $F_1$, the limiting distribution of the properly rescaled largest eigen…

The KPZ universality class contains many stochastic growth models with universal spatial and temporal fluctuations. The Airy process and related Airy line ensembles describe spatia…

KPZ universality conjecture. The Kardar–Parisi–Zhang equation should be a universal scaling limit for stochastic growth fluctuations, including phenomena such as burning fronts, ba…

Growth-rate conjecture. For every $\eta>0$, the limit defining $\beta(\eta)$ exists almost surely and is nontrivial.

Irregular-cluster conjecture. DBM also produces irregular clusters in a similar manner to DLA.

Let a model in the KPZ class have a height function $h$ and initial data $h_0$. Suppose that … Then there are non-universal constants $c$ and $C_\varepsilon$ such that … where…

KPZ convergence conjecture. The solution of the KPZ equation converges to the KPZ fixed point under KPZ scaling.

Consider a broad class of stochastic interface models, with time, space, and fluctuation variables scaled according to the $3:2:1$ exponents. KPZ universality conjecture. A wide ra…

The one-dimensional KPZ universality class comprises random growth models, last passage percolation, directed polymers, and random stirred fluids. Let $h(t,x)$ be the height functi…

Outer-perimeter proportion conjecture. There exists a number $\operatorname{per}_d>0$ such that

Outer-perimeter proportion conjecture. With high probability as $t\rightarrow\infty$,

Let $h(0,t)$ denote the height at the origin at time $t$, and let $c(u)$ be the time-dependent coupling. Define the effective time … Restricting the spectral evolution to the singl…

Strong KPZ universality conjecture. The KPZ fixed point is the universal limit, under the KPZ scaling, for a wide class of growth models characterized by a local slope-dependent gr…

Let $\tilde{w}$ be the parameter appearing in the parametric representation of the KPZ short-time height rate function $\Phi(H)$, and let $H_{c2}(\tilde{w})$ denote its branching p…

A $(1+1)$-dimensional interface growth model is a model of random interface evolution in one spatial dimension and time; an asymmetry parameter measures the model's deviation from…

The one-point height distributions and Fredholm-determinant expressions obtained for the described crossover initial conditions are conjectured to be universal for all models in th…

Let $rho_i$ denote the rescaled radial fluctuation at time $t$, defined by … where $r_i$ is the distance to the origin of a point on the corresponding ball, $r(t)=r_0+vt$ is the fi…