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math.GR2024
Parallel geodesics and minimal stable length of random groups
Tsung-Hsuan Tsai
We show that for any pair of long enough parallel geodesics in a random group with generators at density , there is a van Kampen diagram having only one la…
math.GR2022
Phase transition for the existence of van Kampen 2-complexes in random groups
Tsung-Hsuan Tsai
Gromov showed that (1993) with high probability, every bounded and reduced van Kampen diagram of a random group at density satisfies the isoperimetric inequality $|\partial…
math.GR2021★ 2 cited
Density of random subsets and applications to group theory
Tsung-Hsuan Tsai
Developing an idea of M. Gromov, we study the intersection formula for random subsets with density. The \textit{density} of a subset in a finite set is defined by $dens A :…