  We compute the differential Poisson's ratio of a suspended two-dimensional
crystalline membrane embedded into a space of large dimensionality $d \gg 1$.
We demonstrate that, in the regime of anomalous Hooke's law, the differential
Poisson's ratio approaches a universal value determined solely by the spatial
dimensionality $d_c$, with a power-law expansion $\nu = -1/3 + 0.016/d_c +
O(1/d_c^2)$, where $d_c=d-2$. Thus, the value $-1/3$ predicted in previous
literature holds only in the limit $d_c\to \infty$.
