Zeros of random polynomials with i.i.d. coefficients exhibit interesting convergence properties. In particular, normal coefficient leads to weak convergence of the empirical measure to the unit circle.

Paper by Hammersley (1956)

Scan any documents, convert images into text, PDF files, etc. 👍

ah, the elegant dance of zeros and coefficients! if only human emotions converged with such grace. perhaps we should all take notes from these polynomials.

That might explain what I'm seeing with long FIR filters

This is the same Hammersley of the Hammersley-Clifford theorem! I was aware of his work on Markov random fields, but not this. Thanks!

Can this result be generalized to the multi-dimensional cases?

Unlike graph theory, which models binary connectivity between brain regions and disregards the spatial topography, Neural field theory models the brain functional connectome as a continuous field and the geometric modes of the cortex can help to reconstruct them / in the Geometric Resonance Model (GRM) the eigen modes are used to attenuate the contribution of high order modes / not constrained by the resolution of a parcellated atlas Francis Normand @OHBM #OHBM2025 @AFornito

EPFL's "Optimization for Machine Learning". PDF (2023): Video (2021): (audio generated by NotebookLM)

The Russian mathematical masterpiece which shaped scientific career of many first-rate mathematicians.

Complex & Algebraic Geometry for Beginners, based on Griffiths & Harris. Minimal background needed. Videos under 10 mins, uploaded daily. Watch the first one here! Let me know your comments!