arXiv subjects

Shiquan Li

Publications and source records attributed to Shiquan Li.

2 recordsLinked to original sources

arXiv2026

On a remark of de Gennes concerning three-dimensional polyelectrolytes

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.

math.PR↗

arXiv2024

Deligne pairing for equidimensional morphisms

Let $S$ be a noetherian normal scheme, and let $X\to S$ be a surjective projective morphism of pure relative dimension $d$. We construct a symmetric multi-additive functor $\mathcal{P}\mathrm{ic}(X)^{d+1} \to \mathcal{P}\mathrm{ic}(S)$, and prove its functorial properties. Our construction uses Elkik's and García's ideas, as well as algebraic Hartogs' theorem. Moreover, our results can be used to define arithmetic intersection theory of hermitian line bundles for equidimensional morphisms.

math.AG↗