8 problems

A one-dimensional stochastic system has local interactions, a conserved density or height-gradient field, and a weak asymmetric perturbation of a reversible dynamics. Let…

Consider the stochastic three-dimensional ferrohydrodynamic system described in the paper, with relaxation parameter $bb$ and electric conductivity $c3$. Conductivity conjecture. P…

Small-diffusivity KPZ conjecture. The Kardar–Parisi–Zhang equation should also appear when the diffusivity of the particles' molecular motion is taken to be small, rather than the…

Barraquand–Le Doussal's KPZ conjecture. At a certain distance from the origin, these tail fluctuations should be governed by the Kardar–Parisi–Zhang equation.

Let the $\Omega^{\prime}$-process solution be obtained by taking partial expectations in $\Omega$ of the multiplicative functionals associated to the $DB2^{\prime}$-process. The co…

Consider the one-dimensional viscous Burgers equation … with positive viscosity coefficient, whose inviscid version admits shock and rarefaction waves for Riemann initial data. The…

Let $\mu_A$ denote the invariant measure constructed for the one-dimensional stochastic compressible Navier–Stokes equations with noise amplitude parameter $A$. The unforced system…

Let the fluctuation field be the empirical particle-density discrepancy from the profile predicted by the Smoluchowski coagulation-fragmentation-diffusion PDE, normalized by the sq…