On a remark of de Gennes concerning three-dimensional polyelectrolytes

arXiv:2604.08389v2 Announce Type: replace Abstract: This work is inspired by a remark of de Gennes about polyelectrolytes, which are charged polymers. A common model for a polymer is a self-avoiding or self-repelling random walk or Brownian motion. For polyelectrolytes, the repelling potential is the Coulomb potential arising from pairs of charged particles. We show that in the continuous case of Brownian motion in three dimensions, the spread of the polymer, in particular the the radius of gyration of a polyelectrolyte of length $T$ grows linearly with $T$, up to logarithmic corrections.