5 problems

The mean values of the energy currents are expressed in terms of $eta^{(l)}_j$, with $v^{(l=1)}_k=1$, and the time-averaged correlations are … Here the time evolution up to $t_n$ i…

Bounded-carrier Brownian invariance conjecture. If $S^K$ is the Brownian motion with drift $c>0$ conditioned to stay within $K$ of its past maximum, then

Ferrari's soliton decomposition conjecture. Any invariant measure on configurations can be decomposed into independent measures on solitons of different sizes.

Soliton-component independence conjecture. If $\mu$ is $T$-invariant and $\theta$-mixing, then the $\zeta_k$ are independent over $k$, and each $\zeta_k$ is $\theta$-mixing.

Soliton-component decomposition conjecture. If $\mu$ is shift-mixing and $T$-invariant, then its soliton components should be independent and shift-mixing.