5 problems

Let $J$ be an interaction matrix, and let $\mathcal{T}_v\mu_{N,\rho}$ denote the tilted canonical Ising measure with linear tilt $v$. Write…

Let $\tilde{\chi}^{(n)}$ denote the $n$-particle contribution to the square-lattice Ising susceptibility, and let $k$ range over the lower-index contributions appearing as…

Let $\tilde{\chi}^{(n)}$ be the $n$-particle contribution, and let the lower-index contributions $\tilde{\chi}^{(n-2k)}$ be removed with coefficients $\alpha_{n-2k}$, where…

For each $n$, let $L_n$ be the minimal-order linear differential operator for $\tilde{\chi}^{(n)}$. A direct-sum decomposition means that the operator for a higher-particle contrib…

Let $L_E$ be the linear differential operator corresponding to the complete elliptic integral $E$, and let $L_n$ denote a linear differential operator associated with the $n$-parti…