Year: 2026
Type: preprint
Abstract: Using contour-integral representations of the permanent and of the Hafnian, we turn the computation of their moments for random matrices into a replica calculation, analogous to that of the moments of the partition function of a mean-field spin glass. For the $2k$-th moment of $N\times N$ matrices with independent entries, the dominant saddle point is replica symmetric for $k>2$, and we obtain in closed form the exponential growth rate, the prefactor and the first $1/N$ correction, in agreement with exact enumerations. The growth rate depends only on whether the entries are real or complex; higher cumulants affect only the prefactor and the $1/N$ term. At $k=2$ the replica-symmetric solution becomes unstable, separating a power-law bulk of the distribution from a large-deviation tail, which we compute. The results apply to boson sampling with single photons and with squeezed light.
Source: arXiv (Cornell University)
Institutions: Istituto Nazionale di Fisica Nucleare, Sezione di Bari, University of Bari Aldo Moro, National Agency for New Technologies, Energy and Sustainable Economic Development, The Abdus Salam International Centre for Theoretical Physics (ICTP), Istituto Nazionale di Fisica Nucleare, Sezione di Trieste
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223084987