随机Gromov怪物的发散性和拟isometry类
Divergence and quasi-isometry classes of random Gromov's monsters
摘要：
我们表明，格罗莫夫的怪物产生于i.i.d.扩展器的随机标号（我们称之为随机格罗莫夫怪物）沿着子序列具有线性发散，因此特别是它们不包含莫尔斯拟测地线，并且它们不是由扩展器的图形小消去标号产生的格罗莫夫怪物的准等距。此外，通过进一步研究发散函数，我们表明，有无数个随机Gromov怪物的拟等距类。
英文摘要：
We show that Gromov's monsters arising from i.i.d. random labellings of expanders (that we call random Gromov's monsters) have linear divergence along a subsequence, so that in particular they do not contain Morse quasigeodesics, and they are not quasi-isometric to Gromov's monsters arising from graphical small cancellation labellings of expanders. Moreover, by further studying the divergence function, we show that there are uncountably many quasi-isometry classes of random Gromov's monsters.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
