Free fermions in d dimensions have a hole probability that scales as exp[-(k_F R)^{d+1} Φ_d(u)] with a transition of order 3/2(d+1) in Φ_d at the universal point u_c=2/π, computed exactly via Coulomb gas mapping.
Widom, A theorem on translation kernels in n dimensions, Trans
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A transition in the hole probability at finite temperature for free fermions in $d$ dimensions
Free fermions in d dimensions have a hole probability that scales as exp[-(k_F R)^{d+1} Φ_d(u)] with a transition of order 3/2(d+1) in Φ_d at the universal point u_c=2/π, computed exactly via Coulomb gas mapping.