11 problems

Consider reaction-diffusion processes of the form … where $m$ and $n$ are the orders of creation and removal, while $k$ and $l$ determine additional symmetries such as parity conse…

Let the directed-percolation (DP) and pair-contact process (PCP) models be considered at their steady-state critical transitions, and let $m_n=\langle\rho^n\rangle$ denote order-pa…

Consider the coagulation-fission process with reactions $2A\to 3A$ and $2A\to A$, together with diffusion, including the variants described in the source. Odor's conjecture. The co…

Let the pair-contact process with diffusion (PCPD) be considered at low and high diffusion rates. Odor's conjecture. The PCPD might belong to two different universality classes for…

Let $\theta(t,x)$ denote the random field solving the stochastic advection-diffusion equation under consideration, and consider its behavior in the diffusive scaling regime. Edward…

Brownian Castle universality conjecture. Under these assumptions and scaling, the solution of the random transport equation converges in a weak sense to the Brownian Castle.

Let $v(\cdot)$ be the speed function of a reasonable $(2+1)$-dimensional growth model, and let $H_\rho$ be the Hessian of $v(\cdot)$ computed at the slope $\rho$. Write $\alpha$ fo…

Let ${\mathcal{S}}$ be one of the 19 small-step lattice-path models with finite non-zero orbit sum, and consider its centrally weighted walk model. Let $Q(1,1;t)$ be the correspond…

Branched-polymer universality conjecture. The real model also lies in the universality class of branched polymers.

In the regime where inter-species interactions dominate intra-species interactions, the system has spin excitations with quadratic dispersion above a ferromagnetic ground state, be…

The quintic kernel is defined by … where the $z$- and $\tilde z$-integration paths are appropriate subpaths of the paths shown in the source figure, with the indicated orientation.…