A random link via bridge position is hyperbolic

TL;DR

This paper proves that a randomly generated link via bridge splitting is almost certainly hyperbolic, with probability approaching 1 as the complexity increases.

Contribution

It establishes the asymptotic hyperbolicity of random links constructed through bridge positions, a novel probabilistic result in knot theory.

Findings

Random links via bridge splitting are hyperbolic with probability approaching 1.

The result applies to generic or typical links in the considered model.

Provides a probabilistic foundation for hyperbolic structures in link theory.

Abstract

We show that a random link defined by random bridge splitting is hyperbolic with asymptotic probability 1.