arXiv subjects

M. R. Dennis

Publications and source records attributed to M. R. Dennis.

20 records · Page 2Linked to original sources

arXiv2003

Correlations and screening of topological charges in gaussian random fields

2-point topological charge correlation functions of several types of geometric singularity in gaussian random fields are calculated explicitly, using a general scheme: zeros of $n$-dimensional random vectors, signed by the sign of their jacobian determinant; critical points (gradient zeros) of real scalars in two dimensions signed by the hessian; and umbilic points of real scalars in two dimensions, signed by their index. The functions in each case depend on the underlying spatial correlation function of the field. These topological charge correlation functions are found to obey the first Stillinger-Lovett sum rule for ionic fluids.

math-ph↗

arXiv2002

Saddle points in the chaotic analytic function and Ginibre characteristic polynomial

Comparison is made between the distribution of saddle points in the chaotic analytic function and in the characteristic polynomials of the Ginibre ensemble. Realising the logarithmic derivative of these infinite polynomials as the electric field of a distribution of coulombic charges at the zeros, a simple mean-field electrostatic argument shows that the density of saddles minus zeros falls off as $π^{-1}|z|^{-4}$ from the origin. This behaviour is expected to be general for finite or infinite polynomials with zeros uniformly randomly distributed in the complex plane, and which repel quadratically.

nlin.CD↗