@article{13975,
  abstract     = {We consider the spectrum of random Laplacian matrices of the form Ln=An−Dn where An
 is a real symmetric random matrix and Dn is a diagonal matrix whose entries are equal to the corresponding row sums of An. If An is a Wigner matrix with entries in the domain of attraction of a Gaussian distribution, the empirical spectral measure of Ln is known to converge to the free convolution of a semicircle distribution and a standard real Gaussian distribution. We consider real symmetric random matrices An with independent entries (up to symmetry) whose row sums converge to a purely non-Gaussian infinitely divisible distribution, which fall into the class of Lévy–Khintchine random matrices first introduced by Jung [Trans Am Math Soc, 370, (2018)]. Our main result shows that the empirical spectral measure of Ln  converges almost surely to a deterministic limit. A key step in the proof is to use the purely non-Gaussian nature of the row sums to build a random operator to which Ln converges in an appropriate sense. This operator leads to a recursive distributional equation uniquely describing the Stieltjes transform of the limiting empirical spectral measure.},
  author       = {Campbell, Andrew J and O’Rourke, Sean},
  issn         = {1572-9230},
  journal      = {Journal of Theoretical Probability},
  publisher    = {Springer Nature},
  title        = {{Spectrum of Lévy–Khintchine random laplacian matrices}},
  doi          = {10.1007/s10959-023-01275-4},
  year         = {2023},
}