2 problems

Let $E_r$ be the $r$-th cumulant of the current, let $L$ be the system size, let $x$ be the asymmetry parameter, and let $\rho$ be the density. The intermediate regime is … It lies…

Let $h_r(\Phi)$ be the functions defined by … Here $B_k$ denotes the $k$-th Bernoulli number. Small-$\Phi$ asymptotics conjecture. For every $r\geq3$, … as $\Phi\to0$. This asympto…