9 problems

Weak Kardar–Parisi–Zhang universality conjecture. The density fluctuation fields converge to the solution of the stochastic Burgers equation.

Endo's asymptotic-distribution conjecture. For arbitrary $\Omega$, the probability of configuration $x$ in the asymptotic state is given by

Grazieschi et al.'s mean-field limit conjecture. The mean-field limit of this particle system should have the form of the limiting system obtained by taking $k=1$ and…

McKean's conjecture. The one-dimensional mean-field equation is the Burgers equation.

Universality conjecture. The same generalized large deviation function will be found in other models, such as the symmetric simple exclusion process with pair annihilation at arbit…

Drift non-positivity conjecture. The condition

Consider coagulating Brownian particles in dimension $d\geq 3$, with particle mass $m$ and radius related by $r=m^{\chi}$. Assume that the diffusion coefficients…

Asymptotic absorption-count conjecture. The mean normalized count tends to a constant as $t\to\infty$,

Let an ensemble of particles in $d$ dimensions have masses $m_n$ and evolve according to … Here $N_0$ is the initial number of particles, $M=\sum m_n$ is their total mass, particle…